Related papers: Hyperbolic Sets in Incomplete Tables
We present an information-theoretic framework for understanding overfitting and underfitting in machine learning and prove the formal undecidability of determining whether an arbitrary classification algorithm will overfit a dataset.…
We propose a new statistical procedure able in some way to overcome the curse of dimensionality without structural assumptions on the function to estimate. It relies on a least-squares type penalized criterion and a new collection of models…
The asymptotic log-Harnack inequality is established for several different models of stochastic differential systems with infinite memory: non-degenerate SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As…
We develop algorithms for detecting multiple changepoints in functional data when the number of changepoints is unknown (unsupervised case), when it is specified apriori (supervised case), and when certain bounds are available…
We establish Sobolev type inequalities in the noncommutative settings by generalizing monotone metrics in the space of quantum states, such as matrix-valued Beckner inequalities. We also discuss examples such as random transpositions and…
This research focuses on an innovative task of extracting equations from incomplete data, moving away from traditional methods used for complete solutions. The study addresses the challenge of extracting equations from data, particularly in…
This paper presents a conformal prediction method for classification in highly imbalanced and open-set settings, where there are many possible classes and not all may be represented in the data. Existing approaches require a finite, known…
The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…
This paper presents novel algorithms which exploit the intrinsic algebraic and combinatorial structure of the matrix completion task for estimating missing en- tries in the general low rank setting. For positive data, we achieve results…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
We study the behavior of partially twisted multiple zeta-functions. We give new closed and explicit formulas for special values at non-positive integer points of such zeta-functions. Our method is based on a result of M. de Crisenoy on the…
This paper is a survey of results proved in recent years that pertain to classifying cobounded hyperbolic actions of any group $G$. In other words, we discuss results that allow us to describe the partially ordered set $\mathcal{H}(G)$,…
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous…
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…
This paper introduces a novel oversampling technique designed to improve classification performance on imbalanced datasets. The proposed method enhances the traditional SMOTE algorithm by incorporating convex combination and kernel-based…
We introduce two data completion algorithms for the limited-aperture problems in inverse acoustic scattering. Both completion algorithms are independent of the topological and physical properties of the unknown scatterers. The main idea is…
Hyperbolic spaces have proven to be suitable for modeling data of hierarchical nature. As such we use the Poincare ball to embed sentences with the goal of proving how hyperbolic spaces can be used for solving Textual Entailment. To this…
We investigate the NP-Complete problem SAT and the geometry of its instances. For a particular type that we call {\it non-interlaced formulas}, we propose a polynomial time algorithm for their resolution using graphs and matrices.
The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are…
The paper describes a novel method of sampled-data in space (spatial variable) control of scalar semilinear systems of parabolic and hyperbolic type with unknown parameters and distributed disturbances. A finite set of sampled-data in the…