A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Bayesian approach approximates probability functions of Gaussian mixtures.
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note…
Optimal insurance minimizes ruin probability with non-decreasing functions.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
Evidential Softmax preserves multimodality in sparse probability distributions for generative models.
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically eval…
We consider returns of two Korean stock market indices, KOSPI and KOSDAQ index. Central parts of the probability distribution function of returns are well fitted by the Lorentzian distribution function. However, tail parts of the probability distribution function follow a power law behavior well. We found that the prob…
OPAA estimates probability densities using functional analysis.
The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a reparameterization of the Riemann-Theta Boltzmann machine modelling the original probability…
Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields of statistical science. The dissimilarity between a probability forecast and an outcome is measured by a loss function (scoring rule). Popular example of scoring rule for continuous outcomes is the …
In many applications (in particular information systems, such as pattern recognition, machine learning, cheminformatics, bioinformatics to name but a few) the assessment of uncertainty is essential - i.e., the estimation of the underlying probability distribution function. More often than not, the form of this function…
New discrepancy function compares discrete probability measures considering space geometry.
Implied posterior probability of a given model (say, Support Vector Machines (SVM)) at a point is an estimate of the class posterior probability pertaining to the class of functions of the model applied to a given dataset. It can be regarded as a score (or estimate) for the true posterior probability, which ca…
In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The erro…
This study redefines probability for finite outcomes using axioms and examples.
Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of cond…
In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literat…
PGF kernels analyze spherical data using generalized RBF kernels.
A method for diffusion on probability simplex for generative models.
This paper calculates the exact probability distribution of hypervolume improvement for bi-objective problems.
New acquisition function improves batch Bayesian active learning.
Survey on learning Boolean functions in computational theory.
This research improves demand forecasting by predicting complete probability density functions using machine learning.
New concept of attitude towards probability introduced in risk sharing problems.
NNLMs optimize poorly for word probabilities due to embedding space structure.
Paper introduces symmetric divergence link models for probability distributions.
The paper solves a financial mathematics problem using polytopes and probability measures.
Optimizes functionals on probability space using ICNNs.
New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.
New bounds on continuous random variables' right-tail probabilities.
Exact Bayesian inference for discrete models using probability generating functions.
New KQEs improve probability metrics without mean function constraints.
This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative adversarial networks, variational inference, and actor-critic methods in reinforcement l…
We present a theoretical framework of probabilistic learning derived by Maximum Probability (MP) Theorem shown in the current paper. In this probabilistic framework, a model is defined as an event in the probability space, and a model or the associated event -- either the true underlying model or the parameterized mode…
The consultative papers for the Basel II Accord require rating systems to provide a ranking of obligors in the sense that the rating categories indicate the creditworthiness in terms of default probabilities. As a consequence, the default probabilities ought to present a monotonous function of the ordered rating catego…
In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold and under the assumption that the constant discount rate . More specifical…
In this contribution we derive an explicit formula for the boundary non-crossing probabilities for Slepian processes associated with the piecewise linear boundary function. This formula is used to develop an approximation formula to the boundary non-crossing probabilities for general continuous boundaries. The formulas…
New loss function reduces outage probability in ML-assisted resource allocation.
Method bounds tail probabilities of continuous RVs.
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally c…
New neural networks learn mappings between probability measures and functions.
Quantum probability metrics improve distribution comparison in high dimensions.
We investigate the distribution function and the cumulative probability for Korean household incomes, i.e., the current, labor, and property incomes. For our case, the distribution functions are consistent with a power law. It is also showed that the probability density of income growth rates almost has the form of a e…
We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate of our posterior update rule to the true probability function in…
Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.
Develops methods to find most probable paths on complex manifolds.
The crowdsourcing scenarios are a good example of having a probability distribution over some categories showing what the people in a global perspective thinks. Learn a predictive model of this probability distribution can be of much more valuable that learn only a discriminative model that gives the most likely catego…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal probabilities required in inference and learning. However these variational est…