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Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of independent ...

• MN-PCA discovers the low-rank representation and the noise structure simultaneously.
• Theoretically analyze the error bounds when the noise is matrix normal.
• Develop two algorithms based on the Wasserstein distance and the ...

This paper presents a comprehensive study on the problem of Best Arm Retention (BAR), which requires retaining m arms with the best arm included from n after some trials, in stochastic multi-armed bandit settings. We explore many perspectives of ...

Learning with expert advice and multiarmed bandit are two classic online decision problems which differ on how the information is observed in each round of the game. We study a family of problems interpolating the two. For a vector m = (m₁, ..., m_K) ∈ℕ^K, ...

We prove that the single-site Glauber dynamics for sampling proper q-colorings mixes in O_Δ(nlogn) time on line graphs with n vertices and maximum degree Δ when q>(1+o(1))Δ. The main tool in our proof is the matrix trickle-down theorem developed by ...

The problem of bandit with graph feedback generalizes both the multi-armed bandit (MAB) problem and the learning with expert advice problem by encoding in a directed graph how the loss vector can be observed in each round of the game. The mini-...

We study the approximability of boolean Holant problems with complementarily symmetric constraint functions on cubic graphs. We identify a regime in which the problem admits an FPRAS (fully polynomial-time randomized approximation ...

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [4]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations and implies that the corresponding ...

Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class classification, there ...

The bandit problem with graph feedback, proposed in [Mannor and Shamir, NeurIPS 2011], is modeled by a directed graph G = (V, E) where V is the collection of bandit arms, and once an arm is triggered, all its incident arms are observed. A fundamental ...

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k-uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd < n^o(1) and k ≥ 20 log k + 20 log d + 60, the new ...

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [2]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations, and implies that the corresponding ...

We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second-order recurrence modulo in a couple of exceptional cases. As a ...

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k-uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd<n ^o(1) and k≥ 20logk + 20logd + 60, the new ...

We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second order recurrence modulo a couple of exceptional cases. As a ...

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of $q$-colorings for $k$-uniform hypergraphs with maximum degree $\Delta$ if $k\ge 28$ and $q > 357 \Delta^{\frac{14}{k-14}}$. We also obtain a polynomial-time almost uniform ...

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of q-colorings for k-uniform hypergraphs with maximum degree Δ if k≥ 28 and q > 315Δ^14/k−14. We also obtain a polynomial-time almost uniform sampler if q>798Δ^16/k−16/3. ...

Graph coloring is arguably the most exhaustively studied problem in the area of approximate counting. It is conjectured that there is a fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for counting the number of proper colorings as ...

We introduce a roommate market model, in which 2n people need to be assigned to n rooms, with two people in each room. Each person has a valuation to each room, as well as a valuation to each of other people as a roommate. Each room has a rent shared by ...

Markov Chain Monte Carlo (MCMC) method is a widely used algorithm design scheme with many applications. To make efficient use of this method, the key step is to prove that the Markov chain is rapid mixing. Canonical paths is one of the two main tools to ...

In this paper, we study the Radiation hybrid map construction ( $$\mathsf{{RHMC} }$$ ) problem which is about reconstructing a genome from a set of gene clusters. The problem is known to be $$\mathsf{{NP} }$$ -complete even when all gene clusters are of size two and the corresponding problem (...