arXiv research

We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network learning problem without missing data. To the best of our knowledge, this is the f…

In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand,…

In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a convex optimization problem at every trial. We find exact solution to those optimiz…

Efficient algorithm for matching graphs with community structure.

Algorithm samples from Bingham distribution efficiently.

Paper explores limits of exact inference in structured prediction models.

Two sweeps of the Brennan-Schwartz algorithm solve American options under negative rates.

Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.

New algorithm achieves almost exact graph matching in almost quadratic time.

For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the Čech-de Rham complex. In addition, explicit formulas for such primitive family are presented.

Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically approximate algorithms are used for inference due to the combinatorial number of poss…

In multi-objective Bayesian optimization and surrogate-based evolutionary algorithms, Expected HyperVolume Improvement (EHVI) is widely used as the acquisition function to guide the search approaching the Pareto front. This paper focuses on the exact calculation of EHVI given a nondominated set, for which the existing …

We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call \textit{sparsity-number} here). Using this relation, we propose matrix completion…

We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in $\mathbb R^n$ from $r\cdot \tilde O(n^{1.5})$ randomly observed entries of the tensor…

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in $\mathcal{O}(n\log_2 n)$ operations, where…

Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.

Paper speeds up Gaussian process inference using Matérn kernels.

Exact optimality achieved in distributed mean estimation with shared randomness.

We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with $k$ blocks of equal size. More precisely, we consider a random $d$-uniform hypergraph $H$ with $n$ vertices partitioned into $k$ clusters of size $s = n / k$. Hyperedges $e$ are added independently with probability $p$ if $e$ is…

EKM solves the K-medoids problem in polynomial time.

Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.

We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many leve…

We study rank-1 {L1-norm-based TUCKER2} (L1-TUCKER2) decomposition of 3-way tensors, treated as a collection of $N$ $D \times M$ matrices that are to be jointly decomposed. Our contributions are as follows. i) We prove that the problem is equivalent to combinatorial optimization over $N$ antipodal-binary variables. ii)…

We study graph matching with correlated Gaussian features and find thresholds for exact recovery.

Exact and scalable algorithm for Gaussian process regression with Matérn correlations.

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel $K$ that can be seen as a matrix storing the similarity between points. The diversity comes from the fact that the inclusion probability of a subset is equal to the determinan…

Study exact partition recovery with same-cluster oracle, bounded error.

Paper finds exact recovery threshold in general hypergraph model.

A new method for optimal filtration learning in time-series data analysis.

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on reg…

Exact solver speeds up Weston-Watkins SVM subproblem significantly.

SPPL simplifies probabilistic programming for exact inference.

Develops a diagrammatic method for symplectic filling classifications.

Exact minibatch MH method improves scalability for large datasets.

In this paper we propose an algorithm for exact partitioning of high-order models. We define a general class of $m$-degree Homogeneous Polynomial Models, which subsumes several examples motivated from prior literature. Exact partitioning can be formulated as a tensor optimization problem. We relax this high-order combi…

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sa…

Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average…

Study on ReLU regression with Massart noise, achieving exact parameter recovery.

The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive random sampling. The technique converts an optimization problem into a statisti…

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transf…

Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…

We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult …

We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under certain assumptions, expected run time O(N^(3/2)) in R^d where N is the set size, making it the first sub-quadratic exact m…

Bottom-up algorithms outperform top-down in hierarchical community detection at intermediate levels.

FastDTW is often slower than exact DTW in practical applications.

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors…

EGN optimizes deep neural networks with exact Gauss-Newton for large-scale problems.

Paper shows incorrectness of approximate unlearning definitions and challenges exact unlearning verification.