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In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…

Generative adversarial training can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions, typically neural networks. The discriminator set should be large enough to be able to…

Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…

Projected policy gradient (PPG) is a basic policy optimization method in reinforcement learning. Given access to exact policy evaluations, previous studies have established the sublinear convergence of PPG for sufficiently small step sizes…

The theory of spectral filtering is a remarkable tool to understand the statistical properties of learning with kernels. For least squares, it allows to derive various regularization schemes that yield faster convergence rates of the excess…

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting…

A fundamental challenge in machine learning is the choice of a loss as it characterizes our learning task, is minimized in the training phase, and serves as an evaluation criterion for estimators. Proper losses are commonly chosen, ensuring…

We pose and study a fundamental algorithmic problem which we term mixture selection, arising as a building block in a number of game-theoretic applications: Given a function $g$ from the $n$-dimensional hypercube to the bounded interval…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

In most machine learning training paradigms a fixed, often handcrafted, loss function is assumed to be a good proxy for an underlying evaluation metric. In this work we assess this assumption by meta-learning an adaptive loss function to…

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…

This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and…

We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine then sends an $O(\log(mn))$-length message to a server, at…

In this paper, we demonstrate, both theoretically and by numerical examples, that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the…

The nearest neighbor rule is a classic yet essential classification model, particularly in problems where the supervising information is given by pairwise dissimilarities and the embedding function are not easily obtained. Prototype…

Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…