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There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…
We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…
Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…
We give the first outlier-robust efficient algorithm for clustering a mixture of $k$ statistically separated d-dimensional Gaussians (k-GMMs). Concretely, our algorithm takes input an $\epsilon$-corrupted sample from a $k$-GMM and whp in…
Image restoration has experienced significant advancements due to the development of deep learning. Nevertheless, it encounters challenges related to ill-posed problems, resulting in deviations between single model predictions and…
Distribution learning focuses on learning the probability density function from a set of data samples. In contrast, clustering aims to group similar objects together in an unsupervised manner. Usually, these two tasks are considered…
Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical…
This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
We study the pointwise maximum likelihood estimation rates for a class of Gaussian mixtures that are invariant under the action of some isometry group. This model is also known as multi-reference alignment, where random isometries of a…
We study the problem of partitioning a small sample of $n$ individuals from a mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according to their distributions. Each distribution is described by a vector of allele…
Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…