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This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
We propose to optimize neural networks with a uniformly-distributed random learning rate. The associated stochastic gradient descent algorithm can be approximated by continuous stochastic equations and analyzed within the Fokker-Planck…
Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on…
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…
In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is \emph{asymptotically} equivalent to a stochastic…
Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear…
Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a…
Within a statistical learning setting, we propose and study an iterative regularization algorithm for least squares defined by an incremental gradient method. In particular, we show that, if all other parameters are fixed a priori, the…
Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
Universal supervised learning is considered from an information theoretic point of view following the universal prediction approach, see Merhav and Feder (1998). We consider the standard supervised "batch" learning where prediction is done…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
Monotone learning describes learning processes in which expected performance consistently improves as the amount of training data increases. However, recent studies challenge this conventional wisdom, revealing significant gaps in the…