arXiv research

SGD transitions between maxima and minima with varying time scales.

The paper calculates genus bounds for multibranched surfaces.

Graphical lasso may fail to fit models when data points are insufficient.

The paper finds solutions to a curvature equation using maximum/minimum points of a metric function.

Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we argue that for classiffication tasks, mutual information is a more suitable informa…

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate serious…

Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.

Formula for Bergman kernel of complex hyperbolic manifolds proved.

Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. Th…

New bounds on HOMFLY polynomial for homogeneous links.

The paper explores how over-parameterized linear regression models generalize without violating learning theory principles.

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classificati…

In this paper, we study gradient Ricci expanding solitons $(X,g)$ satisfying $Rc=cg+D^2f,$ where $Rc$ is the Ricci curvature, $c<0$ is a constant, and $D^2f$ is the Hessian of the potential function $f$ on $X$. We show that for a gradient expanding soliton $(X,g)$ with non-negative Ricci curvature, the scalar curva…

The oriented area function $A$ is (generically) a Morse function on the space of planar configurations of a polygonal linkage. We are lucky to have an easy description of its critical points as cyclic polygons and a simple formula for the Morse index of a critical point. However, for planar polygons, the function $A$ i…

Paper analyzes robustness of MDPDE under INH setups.

Efficient adjustment sets found for cost-minimized causal estimations.

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corre…

A new method for SSMF improves upon existing algorithms.

The paper studies batch decompositions of random datasets with probabilistic similarity constraints.

Improved MMD estimator for likelihood-free inference.

New proof given for a functional's minimum condition.

A new method optimizes neural sequence models for better task performance.

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Study on maximum principles for nonlinear equations on Riemannian manifolds.

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexi…

We propose a new indicator for technical analysis. The indicator emphasizes maximums and minimums in price series with inherent smoothing and has a potential to be useful in both mechanical trading rules and chart pattern analysis.

New method improves MMD estimation without convexity assumptions.

Closed-form solutions derived for perpetual options under insider models.

Study shows how networks converge to minimum norm solutions with regularization.

Paper introduces Ddim, a new measure of model complexity, for MDL-based learning and change detection.

Let $(M,g)$ be a compact Ricci-flat 4-manifold. For $p \in M$ let $K_{max}(p)$ (respectively $K_{min}(p)$) denote the maximum (respectively the minimum) of sectional curvatures at $p$. We prove that if $K_{max} (p) \le \ -c K_{min}(p)$ for all $p \in M$, for some constant $c$ with $0 \leq c < \frac{2+\sqrt 6}{4}$, th…

New method finds optimal learning rates for neural nets.

We show that the minimum of asymptotic translation lengths of all point-pushing pseudo-Anosov maps on any one punctured Riemann surface is one.

New 2-spheres of revolution with simple cut locus structures.

Paper proposes quantum methods for optimizing machine learning functions.

Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral u…

Novel method improves load estimation in power grids using anomaly and change point detection.

Study finds minimum growth rate for surface solutions.

When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kerne…

New bounds on ropelength for special alternating knots.

A new DR formulation improves metric learning for faster and more stable performance.

Clustering stocks reduces estimation error in global minimum variance portfolio.

Study entropic regularization of Gaussian measures and processes on Hilbert space.

Paper studies unique interior points and estimates for generalized translating soliton problems.

New insights into matrix factorization show strict saddles have bounded eigenvalues.

This paper shows neural networks can solve complex graph problems efficiently.

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives…

A new hierarchical clustering method selects representative points from sub-minimum-spanning-trees.