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Monocular 3D human pose and shape estimation is an inherently ill-posed problem due to depth ambiguities, occlusions, and truncations. Recent probabilistic approaches learn a distribution over plausible 3D human meshes by maximizing the…

This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…

We present approximate algorithms for performing smoothing in a class of high-dimensional state-space models via sequential Monte Carlo methods ("particle filters"). In high dimensions, a prohibitively large number of Monte Carlo samples…

We study the problem of scheduling $n$ independent moldable tasks on $m$ processors that arises in large-scale parallel computations. When tasks are monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation algorithm for…

A set of piecewise linear functions, called polylines, $P_1,\ldots,P_L$ each with at most $n$ vertices can be simplified into a polyline $M$ with $k$ vertices, such that the Fr\'echet distances $\epsilon_1,\ldots,\epsilon_L$ to each of…

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…

Tolerance estimation problems are prevailing in engineering applications. For example, in modern robotics, it remains challenging to efficiently estimate joint tolerance, \ie the maximal allowable deviation from a reference robot state such…

We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…

In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…

We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…

We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…

K-Medoids(KM) is a standard clustering method, used extensively on semi-metric data.Error analyses of KM have traditionally used an in-sample notion of error,which can be far from the true error and suffer from generalization gap. We…

We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…

We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…