arXiv research

ULFS-KDPE estimates parameters efficiently without influence functions.

A new method for handling missing values in data.

The paper quantifies and attributes uncertainty in complex system simulations.

This paper simplifies finding least favorable priors by reducing dimensionality.

Federated learning was proposed with an intriguing vision of achieving collaborative machine learning among numerous clients without uploading their private data to a cloud server. However, the conventional framework requires each client to leverage the full model for learning, which can be prohibitively inefficient fo…

A GAN method for stochastic boundary conditions in fast dynamics.

Data is one of the essential ingredients to power deep learning research. Small datasets, especially specific to medical institutes, bring challenges to deep learning training stage. This work aims to develop a practical deep multimodal that can classify patients into abnormal and normal categories accurately as well a…

Robust quickest change detection method for unknown score functions.

We study the mixtures of factorizing probability distributions represented as visible marginal distributions in stochastic layered networks. We take the perspective of kernel transitions of distributions, which gives a unified picture of distributed representations arising from Deep Belief Networks (DBN) and other netw…

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…

Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite image. Here the universal lattice denotes the special linear group G=SL_m(Z[x1,..…

Unified analysis of reweighted least-squares algorithms for linear models.

Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the method of auxiliary coordinates (MAC). MAC introduces an auxiliary coordinate for …

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learn…

Test-asset construction affects factor model performance.

There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and irreducible topological spherical bui…

New analysis of Muon and SignSGD on matrix-valued least squares problems.

A method for identifying NPWARX models with arbitrary domains using probabilistic mixture models.

Paper introduces $\ell$-DER for regression tasks using morphological operators and convex-concave procedure.

We applied machine learning to predict whether a gene is involved in axon regeneration. We extracted 31 features from different databases and trained five machine learning models. Our optimal model, a Random Forest Classifier with 50 submodels, yielded a test score of 85.71%, which is 4.1% higher than the baseline scor…

Unified framework proves neural networks' ability to mimic complex tasks.

We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as the visible layer. We show that, within certain parameter domains, deep Boltzmann…

Functional PLS improves prediction and inference for scalar responses from functional predictors.

We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For each m at least 3, we construct an infinite family of pairs of m-manifolds on whic…

We consider a problem of ranking and selection via simulation in the context of personalized decision making, where the best alternative is not universal but varies as a function of some observable covariates. The goal of ranking and selection with covariates (R&S-C) is to use simulation samples to obtain a selection p…

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model…

In this paper, we prove uniform lower bounds on the volume growth of balls in the universal covers of Riemannian surfaces and graphs. More precisely, there exists a constant $δ>0$ such that if $(M,hyp)$ is a closed hyperbolic surface and $h$ another metric on $M$ with $\area(M,h)\leq δ\area(M,hyp)$ then for every radiu…

CNNs identify stock market trend endpoints based on expert opinion.

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and u…

If (M^n, g) is a complete Riemannian manifold with filling radius at least R, then we prove that it contains a ball of radius R and volume at least c(n)R^n. If (M^n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume at most c(n)Volume(M,hyp), then we prove that the universal cover of (M,g…

The study shows how nonnegative Ricci curvature and metric cones imply the existence of abelian subgroups in the fundamental group of open manifolds.

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment proble…

Study a simplified model of multiverse structure with synchronized timelines.

Dual-sPLS improves feature selection and prediction in high-dimensional data.

UVU simplifies value uncertainty quantification in RL.

We show that for a large class of hyperbolic knots and links, we can determine bounds on the volume of the link complement from combinatorial information given by a link diagram. Specifically, there is a universal constant C such that if a knot or link admits a prime, twist reduced diagram with at least 2 twist regions…

We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the …

ESNs trained with Tikhonov least squares approximate ergodic dynamical systems in L2(μ) norm.

If $p : Y \to X$ is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to $p$, from the Teichmüller space ${\cal T}(X)$, for $X$, to ${\cal T}(Y)$ actually extends to an embedding between the Thurston compactification of the tw…

Reduces bounded loss learning to binary classification.

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmuller space is a quasi-isometric embedding for both of the standard metrics. As a …

We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald space of finite volume and bounded nonpositive flag curvature with rank at least $2$ whose universal cover is irreducible, is a locally symmetric space or a locall…

Improves bandit convex optimization with gradient variations.

The study examines the universality of Gaussian data in high-dimensional generalized linear estimation.

Complex-valued neural networks can approximate any continuous function.

Rigidity of $L^2$-spaces on manifolds is characterized.

Paper proposes neural networks for learning functions from sets to graphs.

Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of h…