相关论文: Rate-Distortion for Ranking with Incomplete Inform…

We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…

A causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and a coding theorem is derived. Existence of the minimizing kernel is shown using the topology of weak convergence of probability…

Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…

We study a modification of Kendall's tau-test, replacing his permutations of n different numbers by sequences of length n, where repetition is allowed. In particular, binary sequences are included. Random sequences can be tested.

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

The problem of estimating the information rate distortion perception function (RDPF), which is a relevant information-theoretic quantity in goal-oriented lossy compression and semantic information reconstruction, is investigated here.…

In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…

In some practical learning tasks, such as traffic video analysis, the number of available training samples is restricted by different factors, such as limited communication bandwidth and computation power. Determinantal Point Process (DPP)…

We study the problem of computing the rate-distortion function for sources with feed-forward and the capacity for channels with feedback. The formulas (involving directed information) for the optimal rate-distortion function with…

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…

There is increasing attention to evaluating the fairness of search system ranking decisions. These metrics often consider the membership of items to particular groups, often identified using protected attributes such as gender or ethnicity.…

Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The…

We consider elections where both voters and candidates can be associated with points in a metric space and voters prefer candidates that are closer to those that are farther away. It is often assumed that the optimal candidate is the one…

Consider the following social choice problem. Suppose we have a set of $n$ voters and $m$ candidates that lie in a metric space. The goal is to design a mechanism to choose a candidate whose average distance to the voters is as small as…

Recursive partitioning methods provide computationally efficient surrogates for the Wasserstein distance, yet their statistical behavior and their resolution in the small-discrepancy regime remain insufficiently understood. We study…

Doubly truncated data are found in astronomy, econometrics and survival analysis literature. They arise when each observation is confined to an interval, i.e., only those which fall within their respective intervals are observed along with…

In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is…

Recent studies have introduced the worst-case quantum divergence as a key measure in quantum information. Here we show that such divergences can be understood from the perspective of the resource theory of asymmetric distinguishability,…

This work is concerned with the limiting spectral distribution of rank-based dependency measures in high dimensions. We provide distribution-free results for multivariate empirical versions of Kendall's $\tau$ and Spearman's $\rho$ in a…

Handling digital images is almost always accompanied by a lossy compression in order to facilitate efficient transmission and storage. This introduces an unavoidable tension between the allocated bit-budget (rate) and the faithfulness of…