Related papers: Guessing Revisited: A Large Deviations Approach
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and that a sequences of a general kind can be…
We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically, we assume the following game between Alice and Bob: Alice has a sequence $\bx$ of length $n$. Bob wishes to guess $\bx$, yet he…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…
This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…
In this work we study the set size distribution estimation problem, where elements are randomly sampled from a collection of non-overlapping sets and we seek to recover the original set size distribution from the samples. This problem has…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
In image compression, with recent advances in generative modeling, existence of a trade-off between the rate and perceptual quality has been brought to light, where the perceptual quality is measured by the closeness of the output and…
Relative compression, where a set of similar strings are compressed with respect to a reference string, is a very effective method of compressing DNA datasets containing multiple similar sequences. Relative compression is fast to perform…
In this paper we present a general method for information extraction that exploits the features of data compression techniques. We first define and focus our attention on the so-called "dictionary" of a sequence. Dictionaries are…
Reconstructing a hypothetical recurrence equation from the first terms of an infinite sequence is a classical and well-known technique in experimental mathematics. We propose a variation of this technique which can succeed with fewer input…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has…