Related papers: Discretizing $L_p$ norms and frame theory

In this paper, we present a deterministic algorithm for the closest vector problem for all l_p-norms, 1 < p < \infty, and all polyhedral norms, especially for the l_1-norm and the l_{\infty}-norm. We achieve our results by introducing a new…

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…

Using the asymptotical minimax framework, we examine convergence rates equivalency between a continuous functional deconvolution model and its real-life discrete counterpart over a wide range of Besov balls and for the $L^2$-risk. For this…

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function $\pi\propto\mathrm{e}^{-U}$ is known up to a normalizing constant, which is an important task in…

Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…

In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…

Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for $n$-point subsets of $\ell_p$, for $p >…

It is well known that the two-dimensional Hammersley point set consisting of $N=2^n$ elements (also known as Roth net) does not have optimal order of $L_p$-discrepancy for $p \in (1,\infty)$ in the sense of the lower bounds according to…

The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass…

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…

We study minimax density estimation on the product space $\mathbb{R}^{d_1}\times\mathbb{R}^{d_2}$. We consider $L^p$-risk for probability density functions defined over regularity spaces that allow for different level of smoothness in each…

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality…

We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…

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…

Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…

Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this…

Model selection is central to statistics, and many learning problems can be formulated as model selection problems. In this paper, we treat the problem of selecting a maximum entropy model given various feature subsets and their moments, as…

In this article, we use L$_p$ depth for classification of multivariate data, where the value of $p$ is chosen adaptively using observations from the training sample. While many depth based classifiers are constructed assuming elliptic…

Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…