Related papers: Near-optimal sample compression for nearest neighb…
Probabilistic k-nearest neighbour (PKNN) classification has been introduced to improve the performance of original k-nearest neighbour (KNN) classification algorithm by explicitly modelling uncertainty in the classification of each feature…
This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak…
This work develops algorithms for non-parametric confidence regions for samples from a univariate distribution whose support is a discrete mesh bounded on the left. We generalize the theory of Learned-Miller to preorders over the sample…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
The generalized smooth condition, $(L_{0},L_{1})$-smoothness, has triggered people's interest since it is more realistic in many optimization problems shown by both empirical and theoretical evidence. Two recent works established the…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
We present a new algorithm for general reinforcement learning where the true environment is known to belong to a finite class of N arbitrary models. The algorithm is shown to be near-optimal for all but O(N log^2 N) time-steps with high…
We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every $n$, $d = n^{o(1)}$, and every $d$-dimensional symmetric norm $\|\cdot\|$,…
We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence…
It is generally well understood that predictive classification and compression are intrinsically related concepts in information theory. Indeed, many deep learning methods are explained as learning a kind of compression, and that better…
Most natural language processing tasks can be formulated as the approximated nearest neighbor search problem, such as word analogy, document similarity, machine translation. Take the question-answering task as an example, given a question…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…
We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an…
This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated…