Related papers: Threshold rates for properties of random codes
Large-scale deep learning models are known to memorize parts of the training set. In machine learning theory, memorization is often framed as interpolation or label fitting, and classical results show that this can be achieved when the…
We study the statistical properties of random numbers under the Martin-L\"of definition of randomness, proving that random numbers obey analogues of Strong Law of Large Numbers, the Law of the Iterated Logarithm, and that they are normal.…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
We study the error correcting properties of Haar random codes, in which a $K$-dimensional code space $\boldsymbol{C} \subseteq \mathbb{C}^N$ is chosen at random from the Haar distribution. Our main result is that Haar random codes can…
To solve time inefficiency issue, only potential pairs are compared in string-matching-based source code plagiarism detection; wherein potentiality is defined through a fast-yet-order-insensitive similarity measurement (adapted from…
The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…
Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling…
Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are…
Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…
We design new polynomials for representing threshold functions in three different regimes: probabilistic polynomials of low degree, which need far less randomness than previous constructions, polynomial threshold functions (PTFs) with…
We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result recovers a known upper bound. For symmetric…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
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…
We derive a general formula of the minimum achievable rate for fixed-to-variable length coding with a regular cost function by allowing the error probability up to a constant $\varepsilon$. For a fixed-to-variable length code, we call the…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
The repetition threshold of a class of sequences is the smallest number $r$ such that a sequence from the class contains no repetition with exponent $> r$. We focus on the class $\mathcal{C}_d$ of $d$-ary sequences rich in palindromes. In…
We use p-values as a discrepancy criterion for identifying the threshold value at which a regression function takes off from its baseline value -- a problem that is motivated by applications in omics experiments, systems engineering,…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
Feature hashing, also known as {\em the hashing trick}, introduced by Weinberger et al. (2009), is one of the key techniques used in scaling-up machine learning algorithms. Loosely speaking, feature hashing uses a random sparse projection…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…