Related papers: The Guesswork of Ordered Statistics Decoding: Gues…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary binary linear codes. Inspired by recent proposals that leverage binary linear codebook structure to reduce the number of…
This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…
This manuscript investigates channel capacity under mismatched stochastic likelihood decoding. We derive Feinstein- and Verd\'u-Han-style bounds on the error probability coded communication. These are used to obtain a general…
Verification is a key bottleneck in improving inference speed while maintaining distribution fidelity in Speculative Decoding. Recent work has shown that sequence-level verification leads to a higher number of accepted tokens compared to…
The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are…
Suppose we are given an $n$-dimensional order-3 symmetric tensor $T \in (\mathbb{R}^n)^{\otimes 3}$ that is the sum of $r$ random rank-1 terms. The problem of recovering the rank-1 components is possible in principle when $r \lesssim n^2$…
Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…
Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Given a computable sequence of natural numbers, it is a natural task to find a G\"odel number of a program that generates this sequence. It is easy to see that this problem is neither continuous nor computable. In algorithmic learning…
Subcode-ensemble decoders improve iterative decoding by running multiple decoders in parallel over carefully chosen subcodes, increasing the likelihood that at least one decoder avoids the dominant trapping structures. Achieving strong…
We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate…
A hypergraph consists of a set of nodes along with a collection of subsets of the nodes called hyperedges. Higher-order link prediction is the task of predicting the existence of a missing hyperedge in a hypergraph. A hyperedge…
We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…
Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain…
In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in…