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Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show…

Machine Learning · Computer Science 2019-09-04 Julius Kunze , Louis Kirsch , Hippolyt Ritter , David Barber

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…

Optimization and Control · Mathematics 2019-07-15 Soroosh Shafieezadeh-Abadeh , Daniel Kuhn , Peyman Mohajerin Esfahani

Data uncertainty in practical person reID is ubiquitous, hence it requires not only learning the discriminative features, but also modeling the uncertainty based on the input. This paper proposes to learn the sample posterior and the class…

Computer Vision and Pattern Recognition · Computer Science 2020-07-20 Yan Zhang , Zhilin Zheng , Binyu He , Li Sun

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

Machine Learning · Computer Science 2024-02-08 Pierre Wolinski , Guillaume Charpiat , Yann Ollivier

Bayesian modeling and analysis of the MEG and EEG modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of…

Mathematical Physics · Physics 2008-11-20 Daniela Calvetti , Harri Hakula , Sampsa Pursiainen , Erkki Somersalo

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Machine Learning · Computer Science 2023-01-30 Hongkang Li , Shuai Zhang , Meng Wang

We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…

Machine Learning · Statistics 2024-09-17 Vincent Menden , Yahya Saleh , Armin Iske

We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete…

Machine Learning · Computer Science 2021-10-22 Manuela Girotti , Ioannis Mitliagkas , Gauthier Gidel

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…

Instrumentation and Methods for Astrophysics · Physics 2025-02-11 Gabriel Missael Barco , Alexandre Adam , Connor Stone , Yashar Hezaveh , Laurence Perreault-Levasseur

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…

Optimization and Control · Mathematics 2020-04-13 Oliver R. A. Dunbar , Matthew M. Dunlop , Charles M. Elliott , Viet Ha Hoang , Andrew M. Stuart

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

Econometrics · Economics 2020-06-12 Matteo Mogliani , Anna Simoni

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Image and Video Processing · Electrical Eng. & Systems 2023-06-28 Guanxiong Luo , Mengmeng Kuang , Peng Cao

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

Methodology · Statistics 2010-09-20 Anthony Lee , Francois Caron , Arnaud Doucet , Chris Holmes

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

Image and Video Processing · Electrical Eng. & Systems 2020-06-23 Jaweria Amjad , Zhaoyan Lyu , Miguel R. D. Rodrigues

We derive explicit non-asymptotic PAC-Bayes generalization bounds for Gibbs posteriors, that is, data-dependent distributions over model parameters obtained by exponentially tilting a prior with the empirical risk. Unlike classical…

Machine Learning · Statistics 2026-04-21 Chenyang Wang , Yun Yang

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Machine Learning · Computer Science 2010-10-19 Sham M. Kakade , Shai Shalev-Shwartz , Ambuj Tewari

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

Machine Learning · Statistics 2023-10-30 Youngsoo Baek , Samuel I. Berchuck , Sayan Mukherjee

We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights. We consider the asymptotic limit where the input…

Machine Learning · Statistics 2025-02-10 Antoine Maillard , Emanuele Troiani , Simon Martin , Florent Krzakala , Lenka Zdeborová