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Классификация: Общество. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 8.26. Источник: www.itar-tass.com.Временные ограничения на прием и выпуск воздушных судов введены в аэропорту Тамбова, сообщила Росавиация.
Классификация: Общество. Схожих патентов: 0. Схожих новостей: 10. Тональность: 0. Информативность: 5.62. Источник: ria.ru.Она рассказывает об истории создания храма, его уничтожении нацистами и послевоенном возрождении
Классификация: Общество. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 9.11. Источник: www.itar-tass.com.Вероятность завершения трансфера в ближайшее время оценивается как очень высокая
Классификация: Спорт. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 12.71. Источник: tass.ru.Бывший футболист лондонского "Челси" бельгиец Миши Батшуайи подписал контракт с клубом "Абха" из Саудовской Аравии, сообщается на странице команды в соцсети Х.
Классификация: Спорт. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 5.04. Источник: ria.ru.Еще в январе Международная федерация волейбола (ФИВБ) сняла все ограничения с наших сборных ближайшего резерва - молодежных и юниорских. Однако возможность реально вступить в борьбу с зарубежными соперниками появилась только в августе. В среду, 19 августа, в боснийском городе Мостар девушки начинают первую стадию отбора на финальный турнир чемпионата Европы-2027 до 20 лет, который пройдет в Италии и на Мальте. А 25 августа старт мужской молодежки на аналогичной квалификации в болгарской Софии.
Классификация: Спорт. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 9.9. Источник: rg.ru.Россия вызвала посла Японии в МИД, где дипломату объяснят, как работать в стране пребывания, заявил на пресс-конференции министр иностранных дел РФ Сергей Лавров.
По его словам, дипломат должен прийти в ведомство, чтобы поговорить. Глава ...
Бывший генеральный директор "Спартака" Юрий Заварзин похвалил новичка московской команды Мирилинда Даку. Его слова приводит издание Vprognoze.ru.
"Даку свежую ноту привнес в команду, потому что чистого нападающего у ...
В столице подошел к концу IV Всероссийский детский футбольный турнир «Кубок Московского спорта – Битва школ», в котором приняли участие игроки 2015 года рождения (дети не старше 11 лет).
Классификация: Москва. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 12.07. Источник: aif.ru.В его формировании примет участие египетская сторона, пишет портал
Классификация: Международные. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 9.03. Источник: tass.ru.Посольство России в Польше указало на лживый характер обвинений в якобы "депортации" украинских детей, имеющий место в польской прессе.
Классификация: Международные. Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 4.76. Источник: ria.ru.Президент Дональд Трамп на брифинге попросил журналистку CNN Алайну Трин помолчать и сделал несколько резких комментариев в ее адрес. Видео опубликовал Fox News.
Телеканал передает, что инцидент произошел в понедельник, 17 августа, во ...
Five residential houses, five infrastructure facilities, three trucks, and three passenger cars were damaged
Классификация: . Схожих патентов: 0. Схожих новостей: 9. Тональность: 0. Информативность: 8.62. Источник: tass.com.
Бывший участник группы Стаса Намина «Цветы» 74-летний Владислав Петровский после наезда питбайка во Владимирской области умер в машине скорой помощи, следует из сводки УМВД по региону. «Скончался в автомобиле скорой медицинской помощи», – приводит ТАСС текст сообщения. По данным полиции, ДТП произошло 16 августа около 11.25 мск на улице Проезд Мира в поселке Городищи Петушинского округа. Водитель питбайка «Эндуро» – подросток 2011 года рождения – совершил наезд на велосипедиста 1952 года рождения. В сводке уточняется, что велосипедист пересекал проезжую часть слева направо по ходу движения.Как писала газета ВЗГЛЯД, ранее сообщалось, что Петровский погиб в ДТП с питбайком во Владимирской ...
Пассажирские перевозки Луганск - Украина - Луганск, Луганск - Минск - Луганск.
*Микроавтобусы без пеших переходов через Беларусь/Польшу с загранпаспортом:
Луганск - Киев, Львов, Ровно, Хмельницкий, Винница, Житомир, Потава, Харьков ,Днепр, Николаев, Одесса и обратно.
*Без выезда в ЕС - через поганпереход Мокраны(Беларусь) - Доманово(Украина) с пешим переходом границы (1,5 км).
Луганск - Киев, Харьков, Днепр, Полтава, Николаев, Одесса,
Винница, Житомир.
*Микроавтобусы Луганск - Минск - Луганск.
Также заберём из всех(почти) городов Луганской области.
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Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under marginalization of Gaussian Bayesian networks, and present a graphical structure that faithfully represents margins of Gaussian Bayesian networks. We present the first duality between parameter optimization of a latent variable model and training a feed-forward neural network in the parameter space of the assumed family of distributions. Based on this observation, we develop an algorithm for parameter optimization of these graphical structures using the ...
Text classification is the task of automatically assigning text documents correct labels from a predefined set of categories. In real-life (text) classification tasks, observations and misclassification costs are often unevenly distributed between the classes - known as the problem of imbalanced data. Synthetic oversampling is a popular approach to imbalanced classification. The idea is to generate synthetic observations in the minority class to balance the classes in the training set. Many general-purpose oversampling methods can be applied to text data; however, imbalanced text data poses a number of distinctive difficulties that stem from the unique nature of text compared to ...
In good arm identification (GAI), the goal is to identify one arm whose average performance exceeds a given threshold, referred to as a good arm, if it exists. Few works have studied GAI in the fixed-budget setting when the sampling budget is fixed beforehand, or in the anytime setting, when a recommendation can be asked at any time. We propose APGAI, an anytime and parameter-free sampling rule for GAI in stochastic bandits. APGAI can be straightforwardly used in fixed-confidence and fixed-budget settings. First, we derive upper bounds on its probability of error at any time. They show that adaptive strategies ...
The mean field variational Bayes (VB) algorithm implemented in Stan is relatively fast and efficient, making it feasible to produce model-estimated official statistics on a rapid timeline. Yet, while consistent point estimates of parameters are achieved for continuous data models, the mean field approximation often produces inaccurate uncertainty quantification to the extent that parameters are correlated a posteriori. In this paper, we propose a simulation procedure that calibrates uncertainty intervals for model parameters estimated under approximate algorithms to achieve nominal coverages. Our procedure detects and corrects biased estimation of both first and second moments of approximate marginal posterior distributions induced ...
In probabilistic Latent Semantic Indexing (pLSI), word frequencies across document corpora are modeled through a low-rank factorization of the expected document-term matrix into topic-word and topic-document components. In this paper, we study the estimation of the topic-word matrix under a sparsity structure motivated by Zipf's law: word frequencies within each topic exhibit a rapid empirical decay, with most probability mass concentrated on a small subset of words. Motivated by this observation, we introduce a spectral estimator that adaptively thresholds rare words prior to factorization. We show that the resulting estimator achieves an $\ell_1$-error rate whose dependence on the vocabulary size ...
Hallucinations, defined as instances where Large Language Models (LLMs) generate false or misleading content, pose a significant challenge that impacts the safety and trust of downstream applications. We introduce UQLM, a Python package for LLM hallucination detection using state-of-the-art uncertainty quantification (UQ) techniques. This toolkit offers a suite of UQ-based scorers that compute response-level confidence scores ranging from 0 to 1. This library provides an off-the-shelf solution for UQ-based hallucination detection that can be easily integrated to enhance the reliability of LLM outputs.
We study reserve price optimization in multi-phase second price auctions, where the seller's prior actions affect the bidders' later valuations through a Markov Decision Process (MDP). Compared to the bandit setting in existing works, the setting in ours involves three challenges.
First, from the seller's perspective, we need to efficiently explore the environment in the presence of potentially untruthful bidders who aim to manipulate the seller's policy.
Second, we want to minimize the seller's revenue regret when the market noise distribution is unknown. Third, the seller's per-step revenue is an unknown, nonlinear random variable, and cannot even be directly observed from the ...
Predicting future time-to-event outcomes is a foundational task in statistical learning. While various methods exist for generating point predictions, quantifying the associated uncertainties poses a more substantial challenge. In this study, we introduce an innovative approach specifically designed to address this challenge, accommodating dynamic predictors that may manifest as stochastic processes. Our investigation harnesses the forward intensity function in a novel way, providing a fresh perspective on this intricate problem. The framework we propose demonstrates remarkable computational efficiency, enabling efficient analyses of large-scale investigations. We validate its soundness with theoretical guarantees, and our in-depth analysis establishes the weak convergence of ...
To our knowledge, the analysis of convergence rates for persistence diagrams estimation from noisy signals has predominantly relied on lifting signal estimation results through sup-norm (or other functional norm) stability theorems. We believe that moving forward from this approach can lead to considerable gains. We illustrate it in the setting of nonparametric regression. From a minimax perspective, we examine the inference of persistence diagrams (for the sublevel sets filtration). We show that for piecewise Hölder-continuous functions, with control over the reach of the set of discontinuities, taking the persistence diagram coming from a simple histogram estimator of the signal permits ...
To understand the training dynamics of neural networks, prior studies have considered the mean-field (MF) limit of two-layer NNs as the width tends to infinity, establishing theoretical guarantees for its convergence under gradient flow training as well as approximation and generalization capabilities. In this work, we study the infinite-width limit of a type of three-layer neural network where the first-layer weights are untrained. To rigorously define the limiting model, we extend the MF theory by lifting the representation of neurons from Euclidean to functional spaces. This allows us to establish the MF training dynamics as a functional gradient flow with ...
This work introduces a novel principle for disentanglement we call mechanism sparsity regularization, which applies when the latent factors of interest depend sparsely on observed auxiliary variables and/or past latent factors. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that explains them. We develop a nonparametric identifiability theory that formalizes this principle and shows that the latent factors can be recovered by regularizing the learned causal graph to be sparse, under some assumptions such as the absence of instantaneous causal effects between latent factors. More precisely, we ...
Graph neural networks (GNNs) have become pivotal tools for processing graph-structured data, leveraging the message passing scheme as their core mechanism. However, traditional GNNs often grapple with issues such as instability, over-smoothing, and over-squashing, which can degrade performance and create a trade-off dilemma. In this paper, we introduce a discriminatively trained, multi-layer Deep Scattering Message Passing (DSMP) neural network designed to overcome these challenges. By harnessing spectral transformation, the DSMP model aggregates neighboring nodes with global information, thereby enhancing the precision and accuracy of graph signal processing. We provide theoretical proofs demonstrating the DSMP's effectiveness in mitigating these issues under ...
We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves lower-order differential operators. The Primal-Dual Hybrid Gradient (PDHG) algorithm is then leveraged for this saddle point problem. By introducing suitable precondition operators to the proximal steps in the PDHG algorithm, we obtain an alternative natural gradient ascent-descent optimization scheme for updating the neural network parameters. We apply the Krylov subspace method (MINRES) to evaluate the natural gradients efficiently. Such treatment readily handles the inversion of precondition matrices ...
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the functional covariate and the functional response, and then build a second-layer Hilbert space for the covariate to capture nonlinearity. The second-layer space is assumed to be a reproducing kernel Hilbert space, which is generated by a positive definite kernel determined by the inner product of the first-layer Hilbert space for $X$--this structure is known as the nested Hilbert spaces. We develop estimation procedures to implement the ...
We study decentralized optimization over a network of agents, modeled as an undirected graph and operating without a central server. The objective is to minimize a composite function $f+r$, where $f$ is a (strongly) convex function representing the average of the agents' losses, and $r$ is a convex, extended-value function (regularizer).
We introduce DCatalyst, a unified black-box framework that injects Nesterov-type acceleration into decentralized optimization algorithms. At its core, DCatalyst is an inexact, momentum-accelerated proximal scheme (outer loop) that seamlessly wraps around a given decentralized method (inner loop). We show that DCatalyst attains optimal (up to logarithmic factors) communication and computational ...
Conformal prediction, a powerful framework for constructing prediction intervals for response variables using any regression function estimators, often faces the challenge of producing overly broad intervals with limited target data. In this paper, we study the transfer learning problem in conformal prediction, aiming to improve the precision of the prediction interval of the target data with insufficient data by leveraging related auxiliary source datasets. Allowing for the potential non-exchangeability between source and target datasets, we propose two transfer conformal prediction algorithms designed for scenarios where knowledge of informative source data is either present or absent. Our approach uses conditional Kullback-Leibler ...
Extremile regression, as a least squares analog of quantile regression, is potentially a useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric approaches, may face challenges in high-dimensional settings due to data sparsity, computational inefficiency, and the risk of overfitting. While linear regression, particularly in high-dimensional settings, serves as the foundation for many other statistical and machine learning models due to its simplicity, interpretability, and relatively easy implementation, this paper introduces a novel definition of linear extremile regression along with an accompanying estimation methodology. The regression coefficient estimators of this ...
In recent work concerned with the approximation and expressive powers of deep neural networks, Daubechies, DeVore, Foucart, Hanin, and Petrova introduced a system of piecewise linear functions, which can be easily reproduced by artificial neural networks with the ReLU activation function, and showed that it forms a Riesz basis of $L_2([0, 1])$. Their work was subsequently generalized to the multivariate setting by Schneider and Vybíral. In the work at hand, we show that this system serves as a Riesz basis also for Sobolev spaces $W^s([0,1]^d)$ and Barron classes ${\mathbb B}^s([0,1]^d)$ with smoothness $0\lt s\lt 1$. We apply this fact to ...
The present work aims at proving mathematically that a neural network inspired by biology can learn a classification task thanks to local transformations only. In this purpose, we propose a spiking neural network named CHANI (Correlation-based Hawkes Aggregation of Neurons with bio-Inspiration), whose neurons activity is modeled by Hawkes processes. Synaptic weights are updated thanks to an expert aggregation algorithm, providing a local and simple learning rule. We were able to prove that our network can learn on average and asymptotically. Moreover, we demonstrated that it automatically produces neuronal assemblies in the sense that the network can encode several classes ...
There has been increasing research attention on community detection in directed and bipartite networks. However, these studies often fail to consider the popularity of nodes in different communities, which is a common phenomenon in real-world networks. To address this issue, we propose a new probabilistic framework called the Two-Way Node Popularity Model (TNPM). The TNPM also accommodates edges from different distributions within a general sub-Gaussian family. We introduce the Delete-One-Method (DOM) for model fitting and community structure identification, and provide a comprehensive theoretical analysis with novel technical skills dealing with sub-Gaussian generalization. Additionally, we propose the Two-Stage Divided Cosine Algorithm ...
Corruption is notoriously widespread in data collection. Despite extensive research, the existing literature predominantly focuses on specific settings and learning scenarios, lacking a
unified view of corruption modelization and mitigation. In this work, we develop a general
theory of corruption, which incorporates all modifications to a supervised learning problem,
including changes in model class and loss. Focusing on changes to the underlying probability distributions via Markov kernels, our approach leads to three novel opportunities.
First, it enables the construction of a novel, provably exhaustive corruption framework,
distinguishing among different corruption types. This serves to unify existing models and
establish a consistent nomenclature. Second, it facilitates a ...
This paper explores the theoretical foundations of fair regression under the constraint of demographic parity within the unawareness framework, where disparate treatment is prohibited, extending existing results where such treatment is permitted. Specifically, we aim to characterize the optimal fair regression function when minimizing the quadratic loss. Our results reveal that this function is given by the solution to a barycenter problem with optimal transport costs. Additionally, we study the connection between optimal fair cost-sensitive classification, and optimal fair regression. We demonstrate that nestedness of the decision sets of the classifiers is both necessary and sufficient to establish a form ...
Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret. This variant of the multi-armed bandit problem elegantly amalgamates two of its most ubiquitous objectives: regret minimization and BAI. More precisely, the agent's goal is to identify the best arm with a prescribed confidence level $\delta$, while minimizing the cumulative regret up to the stopping time. Focusing on single-parameter exponential families of distributions, we leverage information-theoretic techniques to establish an instance-dependent lower bound on the expected cumulative regret. Moreover, we present an impossibility result that underscores the tension between cumulative ...
In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs.
Once the mapping has been trained, iid posterior samples are obtained by filtering ...
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner similar to SVMs and limits their applicability in large-scale scenarios. In this paper, we introduce a novel convex SSLM formulation which has been demonstrated to revert to a convex quadratic programming problem for hyperparameter values of interest. Leveraging the convexity of our method, we derive numerous results that are unattainable with traditional nonconvex approaches. We conduct a thorough analysis of how hyperparameters ...
Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data are often accompanied by arbitrary signal corruptions, including missing entries and sparse noise. A fundamental challenge is to reliably extract the meaningful information from corrupted tensor data in a statistically and computationally efficient manner. This paper develops a scaled gradient descent (ScaledGD) algorithm to directly estimate the tensor factors with tailored spectral initializations under the tensor-tensor product (t-product) and tensor singular value decomposition (t-SVD) framework. With ...
In this paper, we introduce a data-augmented nonparametric noise contrastive estimation method to density estimation using deep neural networks. By leveraging the idea of contrastive learning, our density estimator exhibits efficiency with a one-step and simulation-free evaluation process, imposes no constraints on the neural network, and is shown to be consistent and asymptotically automatically normalized. A novel data augmentation procedure allows us to mitigate the influence of the choice of reference distribution on our method. Non-asymptotic upper bounds for the expected $L_{2}$-risk and the expected total variation distance have been established, which achieve minimax optimal rates. Moreover, our new method ...
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are held fixed. We consider a family of BMM algorithms for minimizing nonsmooth nonconvex objectives, where each parameter block is constrained within a subset of a Riemannian manifold. We establish that this algorithm converges asymptotically to the set of stationary points, and attains an $\epsilon$-stationary point within $\widetilde{O}(\epsilon^{-2})$ iterations. In particular, the assumptions for our complexity results are completely Euclidean when the underlying manifold is a product of Euclidean or ...
Modern machine learning methods and the availability of large-scale data have significantly advanced our ability to predict target quantities from large sets of covariates. However, these methods often struggle under distributional shifts, particularly in the presence of hidden confounding. While the impact of hidden confounding is well-studied in causal effect estimation, e.g., instrumental variables, its implications for prediction tasks under shifting distributions remain underexplored. This work addresses this gap by introducing a strong notion of invariance that, unlike existing weaker notions, allows for distribution generalization even in the presence of nonlinear, non-identifiable structural functions. Central to this framework is the ...
This paper studies minimax optimization problems defined over infinite-dimensional function classes of over-parameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear functional equations defined by conditional expectations, where the objective functions are quadratic in the functional spaces. We address (i) the convergence of the stochastic gradient descent-ascent algorithm and (ii) the representation learning of the neural networks. We establish convergence in the mean-field regime by considering the continuous-time, infinite-width limit of the optimization dynamics.
Under this regime, stochastic gradient descent-ascent corresponds to a Wasserstein gradient flow over the space of probability measures defined over ...
Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the likelihood function is downweighted by a regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of $\Xi$-variational approximation and the computational complexity ...
We present skwdro, a Python library for training robust machine learning models.
The library is based on distributionally robust optimization using Wasserstein distances, popular in optimal transport and machine learnings. The goal of the library is to make the training of robust models easier for a wide audience by proposing a wrapper for PyTorch modules, enabling model loss' robustification with minimal code changes. It comes along with scikit-learn compatible estimators for some popular objectives. The core of the implementation relies on an entropic smoothing of the original robust objective, in order to ensure maximal model flexibility. The library is available at ...
Heterogeneous auxiliary information commonly arises in big data due to diverse study settings and privacy constraints. Excluding such indirect evidence often results in a substantial loss of statistical inference efficiency. This article proposes a novel framework for integrating a mixture of individual-level data and multiple external heterogeneous summary statistics by multiplying likelihood functions and confidence densities. Theoretically, we show that the proposed method possesses desirable properties and can achieve statistical efficiency comparable to that of the individual participant data (IPD) estimator, which uses all available individual-level data. Furthermore, we develop a communication-efficient distributed inference procedure for massive datasets with heterogeneous ...
Bayesian hierarchical modeling is a natural framework to effectively integrate data and borrow information across groups. In this paper, we address problems related to density estimation and identifying clusters across related groups, by proposing a hierarchical Bayesian approach that incorporates additional covariate information. To achieve flexibility, our approach builds on ideas from Bayesian nonparametrics, combining the hierarchical Dirichlet process with dependent Dirichlet processes. The proposed model is widely applicable, accommodating multiple and mixed covariate types through appropriate kernel functions as well as different output types through suitable component-specific likelihoods. This extends our ability to discern the relationship between covariates and ...
Penalized empirical risk minimization with a surrogate loss function is often used to learn a high-dimensional linear decision rule in classification problems. Although much of the literature focus on the generalization error, there is a lack of inference procedures for identifying the driving factors of the estimated decision rule, especially when the surrogate loss is non-differentiable. We propose a kernel-smoothed decorrelated score to construct hypothesis tests and interval estimators for a linear decision rule estimated using a piece-wise linear surrogate loss, which has a discontinuous gradient and non-regular Hessian. Specifically, we adopt kernel approximations to smooth the discontinuous gradient near ...
Best Arm Identification (BAI) problems are progressively used for data-sensitive applications, such as designing adaptive clinical trials, tuning hyper-parameters, and conducting user studies. Motivated by the data privacy concerns invoked by these applications, we study the problem of BAI with fixed confidence in both the local and central models, i.e. under $\epsilon$-local and $\epsilon$-global Differential Privacy (DP). First, to quantify the cost of privacy,
we derive lower bounds on the sample complexity of any $\delta$-correct BAI algorithm satisfying$\epsilon$-global DP or $\epsilon$-local DP. Our lower bounds suggest the existence of two privacy regimes. In the high-privacy regime, the hardness depends on a ...
Recent developments of stochastic optimization often suggest biased gradient estimators to improve either the robustness, communication efficiency or computational speed. Representative biased stochastic gradient methods (BSGMs) include Zeroth-order stochastic gradient descent (SGD), Clipped-SGD and SGD with delayed gradients. The practical success of BSGMs motivates a lot of convergence analysis to explain their impressive training behaviour. As a comparison, there is far less work on their generalization analysis, which is a central topic in modern machine learning. In this paper, we present the first framework to study the stability and generalization of BSGMs for convex and smooth problems. We introduce a ...
The Ridgeless minimum $\ell_2$-norm interpolator in overparametrized linear regression has attracted considerable attention in recent years in both machine learning and statistics communities. While it seems to defy conventional wisdom that overfitting leads to poor prediction, recent theoretical research on its $\ell_2$-type risks reveals that its norm minimizing property induces an `implicit regularization' that helps prediction in spite of interpolation.
This paper takes a further step that aims at understanding its precise stochastic behavior as a statistical estimator. Specifically, we characterize the distribution of the Ridgeless interpolator in high dimensions, in terms of a Ridge estimator in an associated Gaussian sequence ...
We present LazyDINO, a transport map variational inference method for fast, scalable, and efficiently amortized solutions of high-dimensional nonlinear Bayesian inverse problems with expensive parameter-to-observable (PtO) maps. Our method consists of an offline phase, in which we construct a derivative-informed neural surrogate of the PtO map using joint samples of the PtO map and its Jacobian as training data. During the online phase, when given observational data, we rapidly approximate the posterior using surrogate-driven training of a lazy map, i.e., a structure-exploiting transport map with low-dimensional nonlinearity. Our surrogate construction is optimized for amortized Bayesian inversion using lazy map variational ...
This paper focuses on approximation and learning performances of deep convolutional neural networks with zero-padding and max-pooling. We prove that, to approximate $r$-smooth function, the approximation rates of deep convolutional neural networks with depth $L$ are of order $ (L/\log L)^{-2r/d} $, which is optimal up to a logarithmic factor. Furthermore, we deduce almost optimal generalization errors for implementing empirical risk minimization over deep convolutional neural networks. Our theoretical results are verified by several numerical experiments to show the power of the convolutional structure, zero-padding and max-pooling.
In this paper, for Markov Decision Processes (MDPs) with standard Borel spaces, (i) we first provide a discretization based approximation method for MDPs with continuous spaces under average cost criteria, and provide error bounds for approximations when the dynamics are only weakly continuous (for asymptotic convergence of errors as the grid sizes vanish) or Wasserstein continuous (with a rate in approximation as the grid sizes vanish) under certain ergodicity assumptions. In particular, we relax the total variation condition given in prior work to weak continuity or Wasserstein continuity. (ii) We provide synchronous and asynchronous (quantized) Q-learning algorithms for continuous spaces ...
Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. We perform a theoretical study where the graph is generated by
a Latent Position Model: each node has a latent position and the probability of connection
depends on the distance between latent positions.
We begin by studying the simplest estimator: averaging the label at all neighboring
nodes. We show that in Latent Position Models this estimator tends to a Nadaraya-Watson
estimator in the latent space, with the same rate of convergence.
One issue with this estimator is that it averages over all neighbors of a node, ...
Local differential privacy has become a central topic in data privacy research, offering strong privacy guarantees by perturbing user data at the source and removing the need for a trusted curator. However, the noise introduced by local differential privacy often significantly reduces data utility. To address this issue, we reinterpret private learning under local differential privacy as a transfer learning problem, where the noisy data serve as the source domain and the unobserved clean data as the target. We propose novel techniques specifically designed for local differential privacy to improve classification performance without compromising privacy: (1) a noised binary feedback-based ...
Multi-relational networks among entities are frequently observed in the era of big data. Quantifying the effects of multiple networks has attracted significant research interest recently. In this work, we model multiple network effects through an autoregressive framework for tensor-valued time series. To characterize the potential heterogeneity of the networks and handle the high dimensionality of the time series data simultaneously, we assume a separate group structure for entities in each network and estimate all group memberships in a data-driven fashion. Specifically, we propose a group tensor network autoregression (GTNAR) model, which assumes that within each network, entities in the same ...
In the framework of the FD (frequent directions) algorithm, we first develop two efficient algorithms for low-rank matrix approximations under the embedding matrices composed of the product of any SpEmb (sparse embedding) matrix and any standard Gaussian matrix, or any SpEmb matrix and any SRHT (subsampled randomized Hadamard transform) matrix. The theoretical results are also achieved based on the bounds of singular values of standard Gaussian matrices and the theoretical results for SpEmb and SRHT matrices. With a given Tucker-rank, we then obtain several efficient FD-based randomized variants of T-HOSVD (the truncated high-order singular value decomposition) and ST-HOSVD (sequentially T-HOSVD), ...
The task of causal representation learning aims to uncover latent higher-level causal variables that affect lower-level observations. Identifying the true latent causal variables from observed data, while allowing instantaneous causal relations among latent variables, remains a challenge, however. To this end, we start with the analysis of three intrinsic indeterminacies in identifying latent variables from observations: transitivity, permutation indeterminacy, and scaling indeterminacy. We find that transitivity acts as a key role in impeding the identifiability of latent causal variables. To address the unidentifiable issue due to transitivity, we introduce a novel identifiability condition where the underlying latent causal model satisfies ...
Complex-valued neural networks potentially possess better representations and performance than real-valued counterparts when dealing with some complicated tasks such as acoustic analysis, radar image classification, etc. Despite empirical successes, it remains unknown theoretically when and to what extent complex-valued neural networks outperform real-valued ones. We take one step in this direction by comparing the learnability of real-valued neurons and complex-valued neurons via gradient descent. We theoretically show that a complex-valued neuron can learn functions expressed by any one real-valued neuron and any one complex-valued neuron with convergence rates $O(t^{-3})$ and $O(t^{-1})$ where $t$ is the iteration index of gradient descent, ...
While advances in machine learning with satellite imagery (SatML) are facilitating environmental monitoring at a global scale, developing SatML models that are accurate and useful for local regions remains critical to understanding and acting on an ever-changing planet. As increasing attention and resources are being devoted to training SatML models with global data, it is important to understand when improvements in global models will make it easier to train or fine-tune models that are accurate in specific regions. To explore this question, we design the first study that explicitly contrasts local and global training paradigms for SatML, through a case ...
We study manifold learning with multidimensional scaling for samples of metric space valued data. By adopting a global version of ISOMAP we obtain low-dimensional Euclidean representations. A key
innovation is that we demonstrate that global Fréchet regression
can be utilized for mapping the elements of a convex set in the Euclidean representation space back to the metric space where the objects reside. We refer to this approach as Fréchet manifold learning and showcase it with
one-dimensional distributions as random objects, equipped with the Wasserstein metric, which is an important special case of our general approach. The
resulting low-dimensional representations mimic ...
The success of machine learning (ML) has been intimately linked with the availability of
large amounts of data, typically collected from heterogeneous sources and processed on
vast networks of computing devices (also called workers). Beyond accuracy, the use of ML
in critical domains such as healthcare and autonomous driving calls for robustness against
data poisoning and some faulty workers. The problem of Byzantine ML formalizes these
robustness issues by considering a distributed ML environment in which workers (storing
a portion of the global dataset) can deviate arbitrarily from the prescribed algorithm.
Although the problem has attracted a lot of attention from a theoretical point of view, its
practical ...
Training deep learning neural networks often requires massive amounts of computational ressources. We propose
to sequentially monitor network predictions to trigger retraining only if the predictions are no longer valid. This can reduce drastically computational costs and opens a door to green deep learning. Our approach is based on the relationship to projected second moments monitoring, a problem also arising in other areas such as computational finance. Various open-end as well as closed-end monitoring rules are studied under mild assumptions on the training sample and the observations of the monitoring period. The results allow for high-dimensional non-stationary time series data and ...
This study proposes and evaluates a novel Bayesian network classifier which can asymptotically estimate the true probability distribution of the class variable with the fewest class variable parameters among all structures for which the class variable has no parent. Moreover, to search for an optimal structure of the proposed classifier, we propose (1) a depth-first search based method and (2) an integer programming based method. The proposed methods are guaranteed to obtain the true probability distribution asymptotically while minimizing the number of class variable parameters. Comparative experiments using benchmark datasets demonstrate the effectiveness of the proposed method.
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit approach to nonparametric density estimation and study them within a statistical framework to analyze their surprising performance. A key challenge in high-dimensional statistical inference is leveraging low-dimensional structures inherent in the data to mitigate the curse of dimensionality. We assume that the underlying density exhibits a low-dimensional structure by factorizing into low-dimensional components, a property common in examples such as Bayesian networks and Markov random fields. ...
A novel approach for generating conditional probabilistic rainfall downscaling at finer scales from deterministic weather variables at coarser scales with temporal and spatial dependence is introduced. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly modelled conditional on the deterministic coarse weather variables. Secondly, a spatial dependency structure is learned to ensure spatial coherence among these distributions.
To learn marginal distributions over rainfall values, we introduce joint generalised neural models that expand generalised linear models with a deep neural network architecture to jointly fit parameters of the distributions.
The spatial dependency structure is modelled using a censored latent Gaussian copula ...
Conditional independence tests (CITs) test for conditional dependence between random variables given a vector of conditioning or confounder variables. As existing CITs are limited in their applicability to complex, high-dimensional variables such as images, we introduce deep nonparametric CITs (DNCITs). The DNCITs combine embedding maps, which extract feature representations of high-dimensional variables, with nonparametric CITs applicable to these feature representations. For the embedding maps, we derive general properties on their parameter estimators to obtain valid DNCITs and show that these properties include embedding maps learned through (conditional) unsupervised or transfer learning. For the nonparametric CITs, appropriate tests are selected and ...
MALA is a popular gradient-based Markov chain Monte Carlo method to access the Gibbs-posterior distribution. Stochastic MALA (sMALA) scales to large data sets, but changes the target distribution from the Gibbs-posterior to a surrogate posterior which only exploits a reduced sample size. We introduce a corrected stochastic MALA (csMALA) with a simple correction term for which distance between the resulting surrogate posterior and the original Gibbs-posterior decreases in the full sample size while retaining scalability. In a nonparametric regression model, we prove a PAC-Bayes oracle inequality for the surrogate posterior. Uncertainties can be quantified by sampling from the surrogate posterior. ...
Policy inference plays an essential role in the contextual bandit problem. In this paper, we use empirical likelihood to develop a Bayesian inference method for the joint analysis of multiple contextual bandit policies in finite sample regimes. The proposed inference method is robust to small sample sizes and is able to provide accurate uncertainty measurements for policy value evaluation. In addition, it allows for flexible inferences on policy comparison with full uncertainty quantification. We demonstrate the effectiveness of the proposed inference method using Monte Carlo simulations and its application to an adolescent body mass index data set.
As machine learning models and datasets continue to grow, developing complex models has become increasingly computationally demanding. Knowledge distillation reduces deployment cost by compressing a large, well-trained teacher model into a compact student model, but it does not address settings where constructing the teacher itself is the bottleneck. Motivated by this challenge, we introduce Knowledge Cascade, a reverse knowledge distillation framework that uses information from a small, inexpensive student model to guide the development of a more complex teacher model. Although this direction is counterintuitive because the teacher typically has greater representational capacity, we show that student-to-teacher transfer can be ...
In this paper, we study the neural exploration strategy for contextual bandits.
The dilemma of exploitation and exploration widely exists in real-world applications such as recommender systems, online advertising, and clinical trials.
Contextual bandits provide principled methods to solve this dilemma, including two prevalent techniques: Thompson Sampling (TS), and Upper Confidence Bound (UCB).
Neural contextual bandits have been studied to adapt to the non-linear reward function, combined with TS or UCB strategies for exploration.
In this paper, we introduce, EE-Net, which is a novel framework to utilize another neural network to learn the potential gain of exploitation neural network for exploration, different from UCB-based ...
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and finally give error estimates for
the predictive mean in various situations.
This paper investigates causal influences between agents linked by a social graph and interacting over time. In particular, the work examines the dynamics of social learning models and distributed decision-making protocols, and derives expressions that reveal the causal relations between pairs of agents and explain the flow of influence over the network. The results turn out to be dependent on the graph topology and the level of information that each agent has about the inference problem they are trying to solve. Using these conclusions, the paper proposes an algorithm to rank the overall influence between agents to discover highly influential ...
Statistically consistent algorithms have been widely employed for dealing with noisy labels. Their objective functions are designed so that minimizing the expected risk on noisy data leads to the same minimizer as minimizing the expected risk on clean data. From the weak law of large numbers, penalizing the variance of losses would reduce the discrepancy between the average loss and the expected risk on the clean data when there is a finite training sample, and the estimation error in the model's parameters can be reduced. Interestingly, we found that the variance of losses needs to be encouraged for label-noise learning. ...
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits, benefit from the stabilizing effect of shrinkage. Our method, Adaptive Forward Stepwise Regression (AFS) addresses the need for sparser models with shrinkage. We show its connection with boosting via a soft-thresholding viewpoint and demonstrate the ease of adapting the method to classification tasks. In both simulations and real data, our method has lower mean squared error and fewer selected features across multiple settings compared to popular ...
The Transformer model is widely used in various application areas of machine learning, such as natural language processing. This paper investigates the approximation of the Hölder continuous function class $\mathcal{H}_{Q}^{\beta}\left([0,1]^{d\times n},\mathbb{R}^{d\times n}\right)$ by Transformers and constructs several Transformers that can overcome the curse of dimensionality. These Transformers consist of one self-attention layer with one head and the softmax function as the activation function, along with several feedforward layers. For example, to achieve an approximation accuracy of $\epsilon$, if the activation functions of the feedforward layers in the Transformer are ReLU and floor, only $\mathcal{O}\left(\log\frac{1}{\epsilon}\right)$ layers of feedforward layers are needed, ...
We study the best-arm identification problem with fixed confidence when contextual (covariate) information is available in stochastic bandits. In each round, we observe contextual information before selecting an arm. The distribution of the reward associated with the selected arm depends on the observed contextual information. We are interested in finding the arm with the maximum mean reward marginalized over the contextual distribution and not the mean reward conditioned on contexts. Our goal is to identify the best arm with a minimal number of samples under a given error probability. First, we derive the instance-specific sample-complexity lower bounds under the contextual ...
For scientific machine learning tasks with a lot of custom code, picking the right Automatic Differentiation (AD) system matters. Our Julia package DifferentiationInterface.jl provides a common frontend to a dozen AD backends, unlocking easy comparison and modular development. In particular, its built-in preparation mechanism leverages the strengths of each backend by amortizing one-time computations. This is key to enabling sophisticated features like sparsity handling without putting additional burdens on the user.
Unsupervised feature selection has drawn wide attention in the era of big data, since it serves as a fundamental technique for dimensionality reduction. However, many existing unsupervised feature selection models and solution methods are primarily designed for practical applications, and often lack rigorous theoretical support, such as convergence guarantees. In this paper, we first establish a novel unsupervised feature selection model based on regularized minimization with nonnegative orthogonality constraints, which has advantages of embedding feature selection into the nonnegative spectral clustering and preventing overfitting. To solve the proposed model, we develop an effective inexact augmented Lagrangian multiplier method, in which ...
We study the dynamics of a continuous-time model of stochastic gradient descent (SGD) for the least-square problem. Indeed, pursuing the work of, we analyze stochastic differential equations (SDEs) that model SGD either in the case of the training loss (finite samples) or the population one (online setting). A key qualitative feature of the dynamics is the existence of a perfect interpolator of the data, irrespective of the sample size. In both scenarios, we provide precise, non-asymptotic rates of convergence to the (possibly degenerate) stationary distribution. Additionally, we describe this asymptotic distribution, offering estimates of its mean, deviations from it, and ...
We revisit the sequential variants of linear regression with the squared loss, classification problems with hinge loss, and logistic regression, all characterized by unbounded losses in the setup where no assumptions are made on the magnitude of design vectors and the norm of the optimal vector of parameters. The key distinction from existing results lies in our assumption that the set of design vectors is known in advance (though their order is not), a setup sometimes referred to as transductive online learning. While this assumption might seem similar to fixed design regression or denoising, we demonstrate that the sequential nature ...
Additive models play an essential role in studying non-linear relationships. Despite many recent advances in estimation, there is a lack of methods and theories for inference in high-dimensional additive models, including confidence interval construction and hypothesis testing. Motivated by inference for non-linear treatment effects, we consider the high-dimensional additive model and make inferences for the function derivative. We propose a novel decorrelated local linear estimator and establish its asymptotic normality. The main novelty is the construction of the decorrelation weights, which is instrumental in reducing the error inherited from estimating the nuisance functions in the high-dimensional additive model. We construct ...
We propose a novel method for estimating heterogeneous treatment effects based on the fused lasso. By first ordering samples based on the propensity or prognostic score, we match units from the treatment and control groups. We then run the fused lasso to obtain piecewise constant treatment effects with respect to the ordering defined by the score. Similar to the existing methods based on discretizing the score, our methods yield interpretable subgroup effects. However, existing methods fixed the subgroup a priori, but our causal fused lasso forms data-adaptive subgroups. We show that the estimator consistently estimates the treatment effects conditional on ...
This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the unknown sparsity parameter in differentially private sparse linear regression (DP-SLR), eliminating the need for prior knowledge of model sparsity, which is a requisite in the existing literature. Next, we develop the DP debiased algorithm that enables privacy-preserving inference on a particular subset of regression parameters. Our proposed method enables privacy-preserving inference on the regression parameters by leveraging the inherent sparsity of high-dimensional linear regression models. Additionally, we address private feature ...
We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respec\-ting the temporal dynamics of the time series distribution.
We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, and the simulation of the SB diffusion yields new synthetic data samples of the ...
Neural collapse (${\cal NC}$) is a phenomenon that emerges at the terminal phase of the training (TPT) of deep neural networks (DNNs). The features of the data in the same class collapse to their respective sample means and the sample means exhibit a simplex equiangular tight frame (ETF). In the past few years, there has been a surge of works that focus on explaining why the ${\cal NC}$ occurs and how it affects generalization. Since the DNNs are notoriously difficult to analyze, most works mainly focus on the unconstrained feature model (UFM). While the UFM explains the ${\cal NC}$ to ...
This paper proposes a method for dimension reduction that preserves information in unsupervised learning with high-dimensional heterogeneous data, specifically targeting change point detection and clustering analysis. Our main strategy is to apply a Corrected Kernel Principal Component Analysis (CKPCA) method to construct the so-called kernel mean embedding deviation subspace. The approach efficiently identifies distributional changes in these dimension reduction subspaces for unsupervised dimension reduction.
For change point detection, we demonstrate that the locations and number of change points in the dimension-reduced subspaces are identical to those in the original data.
Furthermore, we extend this approach to clustering by embedding the original data ...
Understanding the generalization and optimization of neural networks is a longstanding problem in modern learning theory. The prior analysis often leads to risk bounds of order $1/\sqrt{n}$ for ReLU networks, where $n$ is the sample size. In this paper, we present a general optimization and generalization analysis for gradient descent applied to shallow ReLU networks. We develop convergence rates of the order $1/T$ for gradient descent with $T$ iterations, and show that the gradient descent iterates fall inside local balls around either an initialization point or a reference point. Then we develop improved Rademacher complexity estimates by using the activation ...
Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We introduce the notion of linear disparity measures, which are linear functions of a probabilistic classifier; and bilinear disparity measures, which are also linear in the group-wise regression functions. We show that several popular disparity measures---the deviations from demographic parity, equality of opportunity, and predictive equality---are bilinear.
We find the form of Bayes-optimal fair classifiers under a single linear disparity measure, by uncovering a connection with the Neyman-Pearson lemma. For ...
It is becoming increasingly common in regression to train neural networks that model the entire distribution even if only the mean is required for prediction. This additional modeling often comes with performance gains, and the reasons behind the improvement are not fully known. This paper investigates a recent approach to regression, the histogram loss, which involves learning the conditional distribution of the target variable by minimizing the cross-entropy between a target distribution and a flexible histogram prediction. The resulting loss corresponds to a classification loss: a cross-entropy between the outputs and a smoothed label vector. We design theoretical and empirical ...
We consider the problem of density-ratio estimation using Bregman Divergence with Deep ReLU feedforward neural networks (BDD). We establish non-asymptotic error bounds for BDD density-ratio estimators, which are minimax optimal up to a logarithmic factor when the data distribution has finite support. As an application of our theoretical findings, we propose an estimator for the KL-divergence that is asymptotically normal, leveraging our convergence results for the deep density-ratio estimator and a data-splitting method. We also extend our results to cases with unbounded support and unbounded density ratios. Furthermore, we show that the BDD density-ratio estimator can mitigate the curse of ...
Infinitely wide or deep neural networks (NNs) with independent and identically distributed (i.i.d.) parameters have been shown to be equivalent to Gaussian processes. Because of the favorable properties of Gaussian processes, this equivalence is commonly employed to analyze neural networks and has led to various breakthroughs over the years. However, neural networks and Gaussian processes are equivalent only in the limit; in the finite case there are currently no methods available to approximate a trained neural network with a Gaussian model with bounds on the approximation error. In this work, we present an algorithmic framework to approximate a neural network ...
We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding scenario within a given uncertainty set. However, existing work often resorts to some coarse relaxation of the uncertainty set for the sake of tractability, leading to overly conservative estimation of the policy value. In this paper, we propose a general estimator that provides a sharp lower bound of the policy value using convex programming. The generality of our estimator enables various extensions such as sensitivity analysis using f-divergence, model selection with cross validation ...
Since its introduction in 2017, the Transformer has emerged as the leading neural network architecture, catalyzing revolutionary advancements in many AI disciplines. The key innovation in Transformer is a Self-Attention (SA) mechanism designed to capture contextual information. However, stacking up more layers of the same design has failed to produce trainable deeper Transformers. Thus far, various architectural modifications to the original design have been proposed to enable deeper depths for Transformer models, but a thorough understanding of this depth issue remains lacking. In this paper, we conduct a comprehensive investigation to substantiate the claim that the depth problem is caused ...
We consider one-shot distributed learning problems in a reproducing kernel Hilbert space framework. Current results are limited to the least-squares loss and extensions beyond this meet with some significant technical challenges. We establish the optimal rate of distributed learning for some general class of convex loss functions satisfying mild assumptions, using a novel empirical process on the Bregman divergence induced by the loss, which is essential for carrying out a quadratic approximation in the infinite-dimensional space. The empirical process is bounded by relating the Bregman divergence induced by the loss to the supremum norm and the $L^2$-norm of the functions. ...
In this paper, we study second-order algorithms for the convex-concave minimax problem, which has attracted much attention in many fields such as machine learning in recent years. We propose a Lipschitz-free cubic regularization (LF-CR) algorithm for solving the convex-concave minimax optimization problem without knowing the Lipschitz constant. It can be shown that the iteration complexity of the LF-CR algorithm to obtain an $\epsilon$-optimal solution with respect to the restricted primal-dual gap is upper bounded by $\mathcal{O}(\rho^{2/3}\|z_0-z^*\|^2\epsilon^{-2/3})$ , where $z_0=(x_0,y_0)$ is a pair of initial points, $z^*=(x^*,y^*)$ is a pair of optimal solutions, and $\rho$ is the Lipschitz constant. We further ...