arXiv research

The maximum number of maximum cliques in a graph is determined for graphs with at least 15 vertices.

The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…

The study classifies graphs with specific curvature and maximum degree.

We find the maximum mutual information for neural networks and its key determinants.

Two hitherto disconnected threads of research, diverse exploration (DE) and maximum entropy RL have addressed a wide range of problems facing reinforcement learning algorithms via ostensibly distinct mechanisms. In this work, we identify a connection between these two approaches. First, a discriminator-based diversity …

Establishes a boundary maximum principle for varifolds with fixed contact angle.

In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curv…

Maximum likelihood estimation fails to be well-posed in Gaussian process regression.

Note establishes a local maximum principle for Ricci flow under curvature conditions.

Modeling maximum drawdown records in capital markets using PDMP.

We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …

The paper calculates genus bounds for multibranched surfaces.

Improved text summarization using belief propagation on weighted bipartite graphs.

Study proves Maximum Principles for unbounded Riemannian domains.

New maximum score estimators using ReLU functions and deep neural networks.

In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral …

In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity v…

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…

This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operato…

New graphs with maximum degree 4 found to be Ricci-flat.

Paper develops MRCs for supervised classification using generalized maximum entropy.

Maximum Levine-Tristram signature of torus knots follows a reduction formula.

The authors found necessary and sufficient conditions for Samuelson's web to be of maximum rank.

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…

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…

Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.

The study finds a unique systole maximum in non-hyperelliptic surfaces.

Paper finds maximum curvature of Bézier-spline curves.

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probabi…

Proves a principle for one-phase Bernoulli problem minimizers.

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explici…

Enhances power of covariance matrix tests for high-dimensional data.

MGD combines maximum entropy and diffusion methods for efficient sampling.

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

Based on works by Hopf, Weinberger, Hamilton and Evans, we state and prove the strong elliptic maximum principle for smooth sections in vector bundles over Riemannian manifolds and give some applications in Differential Geometry. Moreover, we use this maximum principle to obtain various rigidity theorems and Bernstein …

In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …

Based on ideas of L. Alías, D. Impera and M. Rigoli developed in "Hypersurfaces of constant higher order mean curvature in warped products", we develope a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature est…

The paper presents a method to estimate joint interventional distributions from marginal interventional data.

New research shows the maximum ℓ1-margin classifier doesn't adapt to sparse ground truths.

In many real-world applications, data is not collected as one batch, but sequentially over time, and often it is not possible or desirable to wait until the data is completely gathered before analyzing it. Thus, we propose a framework to sequentially update a maximum margin classifier by taking advantage of the Maximum…

A new method speeds up quantum state estimation.

Paper proposes a new UCB approach for estimating maximum mean.

Consider the Slepian process $S$ defined by $S(t)=B(t+1)-B(t),t\in [0,1]$ with $B(t),t\in \R$ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum $m_{s}=\max_{0\leq u\leq s}S(u)$ certain and the maximum $M_t=\max_{0\leq u\leq t}S(u)$ for $0< s < t$ fixed. Explicit inte…

Study finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.

Proves a theorem in sub-Riemannian geometry using Carnot groups.

Study on maximum principles for nonlinear equations on Riemannian manifolds.

Graphs with maximum degree Δ have at most O(1) equiangular lines for λ < 3/sqrt(2).