arXiv research

This work improves deep neural network probability estimation methods.

Study improves estimation of rare language model outputs.

We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probabili…

The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We argue that this is not a conceptually sound approach and suggest an alternative ba…

Sharp bounds for high-probability estimation of discrete distributions.

Discussing new econophysics methods for volatility and probability density estimation.

New linear algorithms improve wSVMs for multiclass probability estimation.

One of the central themes in the classification task is the estimation of class posterior probability at a new point $\bf{x}$. The vast majority of classifiers output a score for $\bf{x}$, which is monotonically related to the posterior probability via an unknown relationship. There are many attempts in the literature …

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…

Proposes novel wSVMs for sparse learning and accurate probability estimation.

OPAA estimates probability densities using functional analysis.

In many applications, accurate class probability estimates are required, but many types of models produce poor quality probability estimates despite achieving acceptable classification accuracy. Even though probability calibration has been a hot topic of research in recent times, the majority of this has investigated n…

Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.

Paper improves tree probability estimation using stochastic optimization and variance reduction.

This work assesses DNNs for estimating conditional probabilities.

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…

Obtaining accurate and well calibrated probability estimates from classifiers is useful in many applications, for example, when minimising the expected cost of classifications. Existing methods of calibrating probability estimates are applied globally, ignoring the potential for improvements by applying a more fine-gra…

New method estimates and samples high-dimensional probability distributions avoiding optimization and approximation curse.

Method estimates joint probability density from samples using low-rank decomposition and random projections.

A key prerequisite to optimal reasoning under uncertainty in intelligent systems is to start with good class probability estimates. This paper improves on the current best probability estimation trees (Bagged-PETs) and also presents a new ensemble-based algorithm (MOB-ESP). Comparisons are made using several benchmark …

New algorithms estimate and test collision probability with near-optimal sample complexity.

We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns.

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…

We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability measures, is not significantly easier than estimating the probability measures u…

We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation probabilities, 2) the level crossing probabilities, and 3) the level crossing probabilities…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset…

A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a certain class. In this paper, we forge a connection between random forests and ke…

Proposes a neural network method to combine nonprobability and probability survey samples.

We develop a new method to estimate failure probabilities in complex systems.

The softmax representation of probabilities for categorical variables plays a prominent role in modern machine learning with numerous applications in areas such as large scale classification, neural language modeling and recommendation systems. However, softmax estimation is very expensive for large scale inference bec…

New nonparametric estimators improve causal effect estimation.

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on statistical minimax rates for the problem of estimating a probability distribution under W…

Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation

Paper improves VaR risk allocation by avoiding zero probability events.

New insights on active sequential prediction for mean estimation.

NOFIS uses normalizing flows to estimate rare event probabilities more efficiently.

We study how to efficiently estimate average treatment effects (ATEs) using adaptive experiments. In adaptive experiments, experimenters sequentially assign treatments to experimental units while updating treatment assignment probabilities based on past data. We start by defining the efficient treatment-assignment prob…

DoSE improves OOD detection by estimating model probability density.

Focal loss improves classification but not class-posterior probability estimation.

Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.

Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.

We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust estimator of the class probability $P(y|\pmb{x})$. The regularization term meas…

We present a continuous-time maximum likelihood estimation methodology for credit rating transition probabilities, taking into account the presence of censored data. We perform rolling estimates of the transition matrices with exponential time weighting with varying horizons and discuss the underlying dynamics of trans…

In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and…

The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.

New bounds for LDP with heterogeneous privacy levels guaranteeing high probability of accuracy.

Unified high-probability regret bounds for online convex optimisation with randomised gradient estimators.