Related papers: Learning Hard-Constrained Models with One Sample

In this paper, we design efficient algorithms to approximately count the number of edges of a given $k$-hypergraph, and to sample an approximately uniform random edge. The hypergraph is not given explicitly, and can be accessed only through…

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…

We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\Delta$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if…

We consider the problem of learning a non-negative linear classifier with a $1$-norm of at most $k$, and a fixed threshold, under the hinge-loss. This problem generalizes the problem of learning a $k$-monotone disjunction. We prove that we…

In many learning tasks, certain requirements on the processing of individual data samples should arguably be formalized as strict constraints in the underlying optimization problem, rather than by means of arbitrary penalties. We show that,…

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…

In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their…

The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time…

We study the coloring problem: Given a graph G, decide whether $c(G) \leq q$ or $c(G) \ge Q$, where c(G) is the chromatic number of G. We derive conditional hardness for this problem for any constant $3 \le q < Q$. For $q\ge 4$, our result…

Restricted star colouring is a variant of star colouring introduced to design heuristic algorithms to estimate sparse Hessian matrices. For $k\in\mathbb{N}$, a $k$-restricted star colouring ($k$-rs colouring) of a graph $G$ is a function…

We consider models for molecular sequence evolution in which the transition rates at each site depend on the local sequence context, giving rise to a time-inhomogeneous Markov process in which sites evolve under a complex dependency…

Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…

While reinforcement learning (RL) methods that learn an internal model of the environment have the potential to be more sample efficient than their model-free counterparts, learning to model raw observations from high dimensional sensors…

We consider a reinforcement learning setting in which the deployment environment is different from the training environment. Applying a robust Markov decision processes formulation, we extend the distributionally robust $Q$-learning…

Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic approximation (SA) algorithm under Markovian noise, and establish its finite-sample convergence bounds under various stepsizes. Specifically, we show…

The detection problem in statistical signal processing can be succinctly formulated: Given m (possibly) signal bearing, n-dimensional signal-plus-noise snapshot vectors (samples) and N statistically independent n-dimensional noise-only…

We consider the problem of batch multi-task reinforcement learning with observed context descriptors, motivated by its application to personalized medical treatment. In particular, we study two general classes of learning algorithms: direct…

Combinatorial optimisation problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft…

Let $G(n,m)$ be the random graph on $n$ vertices with $m$ edges. Let $d=2m/n$ be its average degree. We prove that $G(n,m)$ fails to be $k$-colorable with high probability if $d>2k\ln k-\ln k-1+o_k(1)$. This matches a conjecture put forward…

Despite recent advancements in deep learning-based automatic colorization, they are still limited when it comes to few-shot learning. Existing models require a significant amount of training data. To tackle this issue, we present a novel…