Related papers: Discontinuous information in the worst case and ra…

This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed…

We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either…

It is known that, for systems of initial-value problems, algorithms using adaptive information perform much better in the worst case setting than the algorithms using nonadaptive information. In the latter case, lower and upper complexity…

In the worst-case distributed source coding (DSC) problem of [1], the smaller cardinality of the support-set describing the correlation in informant data, may neither imply that fewer informant bits are required nor that fewer informants…

While much work on deep latent variable models of text uses continuous latent variables, discrete latent variables are interesting because they are more interpretable and typically more space efficient. We consider several approaches to…

We consider analytic functions from a reproducing kernel Hilbert space. Given that such a function is of order $\epsilon$ on a set of discrete data points, relative to its global size, we ask how large can it be at a fixed point outside of…

We study approximation and integration problems and compare the quality of optimal information with the quality of random information. For some problems random information is almost optimal and for some other problems random information is…

We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so…

Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…

We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is…

Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…

Conventional distributed approaches to coverage control may suffer from lack of convergence and poor performance, due to the fact that agents have limited information, especially in non-convex discrete environments. To address this issue,…

We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…

This paper studies the differentiability of the value function of switched linear systems under arbitrary switching and controlled switching, referred to as worst-case and optimal value functions respectively. First, we show that the value…

Data processing lower bounds on the expected distortion are derived in the finite-alphabet semi-deterministic setting, where the source produces a deterministic, individual sequence, but the channel model is probabilistic, and the decoder…

We consider approximation problems for tensor product and additive random fields based on standard information in the average case setting. We also study the probabilistic setting of the mentioned problem for tensor products. The main…

In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points often belong to the same or similar classes, and more generally, classification rules of high accuracy…

In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like…

The Predictive Information is the mutual information between the past and the future, I(X_past; X_future). We hypothesize that capturing the predictive information is useful in RL, since the ability to model what will happen next is…