Related papers: Empirical risk minimization and complexity of dyna…
This paper addresses the challenge of identifying a minimal subset of discrete, independent variables that best predicts a binary class. We propose an efficient iterative method that sequentially selects variables based on which one…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…
We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
We consider a general model for high-dimensional empirical risk minimization whereby the data $\mathbf{x}_i$ are $d$-dimensional Gaussian vectors, the model is parametrized by $\mathbf{\Theta}\in\mathbb{R}^{d\times k}$, and the loss depends…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non-stationary…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
Fitting a graphical model to a collection of random variables given sample observations is a challenging task if the observed variables are influenced by latent variables, which can induce significant confounding statistical dependencies…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually…
We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample-complexity of an imitation learning task? We provide the…
We study discrete dynamics governed by a difference inclusion whose increment is the sum of a selection from a set-valued map and a noise term. For any bounded realization, convergence follows once the inter-iterate diameter is controlled…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…