arXiv research

Probabilistic proof of smooth boundaries in optimal stopping problems.

Probabilistic proof shows separability in free groups.

Probabilistic method proves gap estimates on sphere.

New bound on partition function proves Kähler-Einstein stability.

This research simplifies verification of machine learning systems using reparameterization.

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results achieved by other investigators.

Adapts pivoting technique to circle homeomorphisms for proofs.

Stein's method improves probabilistic inference and learning.

New theorem connects probabilistic permanental point processes to Monge-Ampère equation.

In this short note we outline a simple probabilistic proof of the Gauss-Bonnet formula for compact Riemannian manifolds with boundary, which adapts to this setting an argument due to Hsu \cite{Hs1,Hs2} in the closed case. The new technical ingredient is the Feynman-Kac formula for differential forms satisfying absolute…

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the…

NP-HMC extends HMC for nonparametric models in probabilistic programming.

Short proof shows wealth condensation in trading model.

Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.

This paper introduces a neural operator for probabilistic conditioning.

New scoring rules improve probabilistic classification model evaluation.

Simplifies efficient estimation via automatic differentiation and probabilistic programming.

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic mar…

We present a derivation and theoretical investigation of the Adams-Bashforth and Adams-Moulton family of linear multistep methods for solving ordinary differential equations, starting from a Gaussian process (GP) framework. In the limit, this formulation coincides with the classical deterministic methods, which have be…

Invites probabilistic approach to Kähler-Einstein metrics via random point processes.

This work proposes an unsupervised neural network framework for solving combinatorial optimization problems on graphs.

Majority-of-Three is Optimal

We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develo…

We prove that on a closed surface of genus $g$, the cardinality of a set of simple closed curves in which any two are non-homotopic and intersect at most once is $\lesssim g^2 \log(g)$. This bound matches the largest known constructions to within a logarithmic factor. The proof uses a probabilistic argument in graph th…

Novel technique reduces Bayesian network complexity while preserving inference accuracy.

We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our main result holds true for any smooth measure on the manifold, but it has a spec…

Elton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable under the curvature conditions $-C e^{2-η}r(x) \leq K_M(x)\leq -1$ with $η>0$. We give an analytical proof of the same statement. In addition, using this new approach we are able to establish two boundary Harnack i…

The purpose of this paper is to give a new proof of results of Moscovici and Stanton on the orbital integrals associated with eta invariants on compact locally symmetric spaces. Moscovici and Stanton used methods of harmonic analysis on reductive groups. Here, we combine our approach to orbital integrals using the hypo…

Generative models' ELBOs converge to entropy sums, proving for various models.

Trajectory or behavior prediction of traffic agents is an important component of autonomous driving and robot planning in general. It can be framed as a probabilistic future sequence generation problem and recent literature has studied the applicability of generative models in this context. The variety or Minimum over …

We prove that on a closed, orientable surface of genus $g$, a set of simple loops with the property that no two are homotopic or intersect in more than $k$ points has cardinality $\lesssim_k g^{k+1} \log g$. The bound matches the size of the largest known construction to within a factor of $\sim_k \log g$. It generaliz…

Deep neural nets solve high-dim PDEs with boundary conditions.

This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a…

New OLO algorithms use Stein's method for better performance tradeoffs.

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static data analysis. In 2014, Dwork, Feldman, Hardt, Pitassi, Reingold and Roth introd…

Probabilistic deep learning uses neural networks and models to handle uncertainty.

DLPM replaces Gaussian noise with α-stable noise in DDPM, improving data distribution coverage and robustness.

Proposes a new metric learning method for image recognition.

There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for w…

Off-policy reinforcement learning with eligibility traces is challenging because of the discrepancy between target policy and behavior policy. One common approach is to measure the difference between two policies in a probabilistic way, such as importance sampling and tree-backup. However, existing off-policy learning …

CheXpert++ improves CheXpert's accuracy and usability for medical radiology reports.

LinConTS improves regret and constraint violations in probabilistic linearly constrained bandits.

Paper shows ERM's suboptimality due to bias, not variance.

We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic probabilistic programs allow straightforward specification and efficient inference …

Transformers interpret as probabilistic mixtures, offering new insights.

Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate probabilistic inference were feasible, and (ii) small or medium-sized data sets which fit …

Improves probabilistic programming by analyzing program structure.

The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by varying the parameter the corresponding solutions converge to the price of an American…