We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generali…
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48 results for “conditional probabilities”
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability forms. The biggest obstacle of the probability model is the probability distribu…
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…
Convolutional Bayesian filtering generalizes state estimation by incorporating inequality conditions.
problem Standard Bayesian filtering assumes exact conditional probabilities, limiting its applicability.
method Introducing inequality conditions transforms conditional probabilities into convolutional forms, expanding the filtering framework.
result Convolutional Bayesian filtering encompasses standard Bayesian filtering and allows for more nuanced model consideration.
A new method quantizes conditional probability measures using deep learning.
problem Quantizing conditional probability measures efficiently.
method DCMQ method using Huber-energy kernel and deep neural network.
result Promising results on various 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…
This paper uses multivariate probability models to assess financial system risks.
problem Assessing systemic risk in financial systems.
method Computes multivariate conditional probability distributions for elliptical distributions, focusing on Student-t and Normal models.
result Proposes measures of stress impact and systemic risk.
We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distribution of returns.
NCP uses neural networks to efficiently learn conditional distributions.
problem Learning conditional distributions for statistical inference.
method Neural Conditional Probability (NCP) approach.
result NCP efficiently handles complex probability distributions and matches leading methods.
This work assesses DNNs for estimating conditional probabilities.
problem Lack of uncertainty characterization in DNNs for probabilistic applications.
method Investigates DNNs' ability to estimate conditional probabilities using synthetic and real-world datasets.
result DNNs' precision in estimating conditional probabilities is influenced by probability density and inter-categorical sparsity.
Paper improves VaR risk allocation by avoiding zero probability events.
problem Computing VaR contributions for zero probability events.
method Reformulates Euler contributions to a ratio of conditional expectations with strictly positive probability events.
result Proposed estimator outperforms standard Monte Carlo methods in bias and variance.
New method estimates and samples high-dimensional probability distributions avoiding optimization and approximation curse.
problem Estimating high-dimensional probability distributions from data samples.
method Hierarchic probability flow from coarse to fine scales, defined by conditional probabilities across scales.
result Sampling hierarchic models avoids critical slowing down at phase transitions and generates turbulence and dark matter images.
Generative model learns conditional distributions on collective variable levels.
problem Modeling conditional probability distributions on collective variable levels.
method General and efficient learning approach, data enrichment strategy.
result Effective generative models on different level-sets of collective variables.
This paper improves learning uncertain Bayesian networks from incomplete data.
problem Learning conditional probabilities in Bayesian networks with limited data.
method Develops methods to estimate and quantify uncertainty in conditional probabilities with incomplete data.
result Improves state-of-the-art approaches for handling uncertain Bayesian networks with incomplete data.
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parame…
Study generalizes property elicitation to imprecise probabilities.
problem Minimizing risk over imprecise probability distributions.
method Maximin risk minimization over a set of imprecise probabilities.
result Conditions for elicitability of IP-properties.
We consider the following conditional linear regression problem: the task is to identify both (i) a -DNF condition and (ii) a linear rule such that the probability of is (approximately) at least some given bound , and minimizes the loss of predicting the target in the distribution of …
New CPS model tackles conditional probability shift in machine learning.
problem Discrepancy between source and target distributions in machine learning.
method Conditional Probability Shift Model (CPSM) using multinomial regression and EM algorithm.
result Superior balanced classification accuracy on target data compared to existing methods.
Simplifies machine learning validation using kNN and conditional probability algorithms.
problem Validating machine learning models in practical applications.
method Reformulated regression and classification problems using kNN and conditional probability algorithms.
result Online capability and reduced memory usage compared to kNN.
New method for generating images with conditional probability models.
problem Generating images with specific conditions.
method Score-based diffusion models with theoretical analysis and new estimator.
result New estimator for conditional score performs similarly to state-of-the-art.
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…
SGD converges with positive probability for non-convex deep neural networks under specific conditions.
problem Convergence of SGD for non-convex deep neural networks.
method Established local convergence with positive probability under local Łojasiewicz condition and additional structural assumption.
result SGD converges with positive probability for non-convex deep neural networks under specific conditions.
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a universal computational procedure for probabilistic inference. We investigate the com…
The semantic map calibrates uncertainty from language model probabilities.
problem Uncertainty in language model probabilities for professional decisions.
method Prespecified semantic map linking probabilities of verbal responses to probabilities of declared states.
result Language-derived probabilities outperform printed numerical probabilities and recover valid uncertainty coverage.
We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class . The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular …
For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability.
We present a simple approach to forecasting conditional probability distributions of asset returns. We work with a parsimonious specification of ordered binary choice regression that imposes a connection on sign predictability across different quantiles. The model forecasts the future conditional probability distributi…
We extend Bayes' theorem for upper probabilities considering likelihood uncertainty.
problem Addressing uncertainty in likelihood for upper probability bounds.
method Generalization of Wasserman and Kadane's result, considering both prior and likelihood uncertainty.
result A sufficient condition for the upper bound to become an equality.
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of th…
Bayesian approach approximates probability functions of Gaussian mixtures.
problem Approximating probability functions of non-spherical Gaussian mixtures.
method Bayesian decomposition, spherical radial decomposition, random sampling.
result Established differentiability and integral representation of gradient for probability functions.
Proposes a new model for joint probability distributions in computer vision.
problem Limitation of existing models in meeting diverse downstream tasks.
method Uses parametric conditional probability distributions for each group of variables conditioned on the rest.
result Models can be used for any downstream task without task-specific design.
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.
problem Adapting optimal transport for -contaminated sets.
method Generalized optimal transport problems with lower probabilities, showing equivalence under -contaminations.
result Monge's and Kantorovich's problems coincide under -contaminated sets, but not always.
New formula for portfolio risk management using conditional PDEs.
problem Optimal diversification and risk management of portfolios.
method Closed-form formula for conditional probability, Gaussian copulas, conditional risk-neutral PDE.
result Dynamic monitoring of portfolio volatilities and weights from PDEs.
In-Context Learning as Nonparametric Conditional Probability Estimation: Risk Bounds and Optimalitystat.ML
Paper analyzes risk bounds for in-context learning in multiclass classification.
problem Risk bounds for in-context learning in multiclass classification.
method Formalizes tasks as sequences of labeled examples and queries, estimates conditional class probabilities, establishes oracle inequality for KL divergence.
result ICL achieves minimax optimal rate for conditional probability estimation.
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert spaces (RKHSs) by providing a linear-algebraic relation for the kernel mean embedd…
Identifies conditions for multiple invariant probabilities in Markov kernels.
problem Global irreducibility and recurrence do not guarantee uniqueness of invariant probabilities.
method Uses Jordan decomposition of the difference of two invariant probabilities.
result A Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition.
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying value and moment of time. We consider time evolution of this probability distributi…
Study completes financial markets in complex models without external probabilities.
problem Completing financial markets in models without exogenous probability measures.
method Obtained a necessary and sufficient condition for market extension.
result A condition for market extension in complex models is established.
To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are inconsistent. In particular, we would like to present that the constrained quadratic …
It is known that describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, Bayesian tensor network (BTN) is proposed to efficiently capture the conditional probabilities of multiple sets of events with polynomial complexity. BTN is a directed acyclic graphical …
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is intractable, we show how to compute upper and lower bounds on many probabilities of intere…
New technique for multiple-source adaptation without density estimation.
problem Multiple-source adaptation problem.
method Discriminative technique that uses conditional probabilities from unlabeled data.
result Our technique outperforms previous generative solutions and other domain adaptation baselines.
Hierarchical Multinomial-Dirichlet model for the estimation of conditional probability tablesstat.ML
We present a novel approach for estimating conditional probability tables, based on a joint, rather than independent, estimate of the conditional distributions belonging to the same table. We derive exact analytical expressions for the estimators and we analyse their properties both analytically and via simulation. We …
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
Refined analysis of Mitra's algorithm for discrete mixtures.
problem Classifying general discrete mixture distribution models.
method Spectral clustering tailored to bipartite stochastic block models.
result Improved separation conditions for probability distributions.
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation of conditional probability tables for the nodes in the Bayesian network, that we…
Paper constructs unfaithful probability distributions in binary causal graphs.
problem Unfaithful probability distributions in binary causal graphs.
method Constructs unfaithful probability distributions in binary causal graphs.
result Examples of unfaithful probability distributions in binary causal graphs.