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Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
In this paper we propose a theory of contact invariants and open string invariants, which are generalizations of the relative invariants. We introduce two moduli spaces $\bar{\mathcal{M}}_{A}(M^{+},C,g,m+\nu,{\bf y},{\bf…
Artificial neural networks are powerful models, which have been widely applied into many aspects of machine translation, such as language modeling and translation modeling. Though notable improvements have been made in these areas, the…
In this paper, we report recent improvements to the exemplar-based learning approach for word sense disambiguation that have achieved higher disambiguation accuracy. By using a larger value of $k$, the number of nearest neighbors to use for…
We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi…
The extension of nonlinear higher-spin equations in d=4 proposed in [arXiv:1504.07289] for the construction of invariant functional is shown to respect local Lorentz symmetry. The equations are rewritten in a manifestly Lorentz covariant…
We investigate corrections to scaling induced by irrelevant operators in randomly diluted systems near the percolation threshold. The specific systems that we consider are the random resistor network and a class of continuous spin systems,…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine-learning energy models of solids and molecules. This allows us to describe, on the same…
Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many…
We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…
The use of formal analysis tools on models or source code often requires the availability of auxiliary invariants about the studied system. Abstract interpretation is currently one of the best approaches to discover useful invariants,…
In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the…
We compute the Dijkgraaf-Witten invariants of surfaces in terms of projective representations of groups. As an application we prove that the complex Dijkgraaf-Witten invariants of surfaces of positive genus are positive integers.
In this paper we analyze the approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley-Wiener space $\mathcal{PW}_{\pi}^{1}$. It is known that there exist…
In this paper we study random iterated function systems. Our main result gives sufficient conditions for an analogue of a well known theorem due to Khintchine from Diophantine approximation to hold almost surely for stochastically…
We give an alternative proof of a recent result by T.D. Browning and A. Haynes (arXiv:1204.6374v1) on multiplicative inverses in sequences of intervals and improve this result under additional conditions on the spacing of these intervals.