This paper uses RBM to calculate conditional probabilities for nonlinear system identification.
problem Challenges in obtaining probability distributions for nonlinear system identification.
method Modified RBM to calculate joint, input, and conditional probabilities.
result The method outperforms other black-box models in noisy, complex systems.
A new framework for probabilistic learning using Maximum Probability Theorem.
problem Challenges in defining and quantifying model probabilities in probabilistic learning.
method Introduces a new probabilistic framework based on Maximum Probability Theorem, defining models as events with quantified probability measures.
result The probability of a model is invariant to reparameterization and depends solely on the likelihood function.
Probability calibration trees improve accuracy of probability estimates.
problem Improving accuracy and calibration of probability estimates from classifiers.
method Probability calibration trees modify logistic model trees to learn different models in regions of the input space.
result Probability calibration trees outperform isotonic regression and Platt scaling in terms of root mean squared error.
Tutorial on estimating SVM class probabilities.
problem Estimating class probabilities for SVM models.
method Compute implied posterior probabilities via isotonic regression.
result Calibrated implied posterior probabilities for SVMs.
Study improves estimation of rare language model outputs.
problem Estimating probabilities of rare outputs in language models.
method Importance sampling vs. activation extrapolation for low probability estimation.
result Importance sampling outperforms activation extrapolation.
The study evaluates Bregman divergences for learning crowd probabilities.
problem Learning crowd probabilities from global perspectives.
method Adapting machine learning models to target probability distributions using Bregman divergences.
result Special attention is needed when constructing objective functions for neural network optimization.
TensorFlow Probability introduces JointDistributions for probabilistic programming.
problem Specifying models in probabilistic programming languages.
method Declarative representations of directed graphical models.
result JointDistributions for TensorFlow Probability.
New concept of attitude towards probability introduced in risk sharing problems.
problem Risk sharing problems and attitudes towards probability.
method Generalized definition of probability premium, local approximation, rank-dependent utility model, dual theory.
result Attitude towards probability can be first-order or second-order, depending on the model.
A method for diffusion on probability simplex for generative models.
problem Tension between continuous and discrete data in diffusion models.
method Proposes using softmax function applied to Ornstein-Uhlenbeck Process on probability simplex.
result Method extends to bounded image generation.
New probability path model improves flow matching forecasting performance.
problem Impact of probability path model selection on flow matching forecasting performance.
method Proposed a novel probability path model designed to improve forecasting performance.
result Our model achieves faster convergence during training and improved predictive performance compared to existing models.
Binary classification models get more efficient predictive probabilities.
problem Computing predictive probabilities in Bayesian probit models is computationally challenging.
method Use of expectation propagation (EP) to find a closed-form expression for predictive probabilities.
result Closed-form predictive probabilities improve over existing methods.
Conditional probabilities modeled using Riemann-Theta Boltzmann Machines.
problem Modeling conditional probabilities in Boltzmann machines.
method Deriving conditional density functions from Riemann-Theta Boltzmann machines.
result Conditional densities can be directly inferred from Riemann-Theta Boltzmann machines.
This work improves deep neural network probability estimation methods.
problem Estimating probabilities from high-dimensional data with inherent uncertainty.
method Investigates and compares methods for probability estimation using deep neural networks, proposing a new method that promotes consistent probabilities.
result The new method outperforms existing approaches on most metrics on simulated and real-world data.
Bayesian method for high-dimensional categorical data analysis.
problem Difficulties in probability modeling for high-dimensional data.
method Bayesian learning of clique tree structure.
result Optimal clique tree structure for probability modeling.
The paper addresses probability calibration for incomplete sequences.
problem Improving probability estimates from incomplete sequences.
method Adapting traditional calibration techniques to sequences of varying lengths.
result Proposed methods improve probability calibration for modern sequential models.
Models predict probabilities of causation from limited data.
problem Estimating probabilities of causation requires unreliable or impractical experimental and observational data.
method Proposed Exact-MLP and Mask-MLP models trained on reliable subpopulations.
result Models achieve average MAEs of roughly 0.03, reducing MAE by 80%.
Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.
problem Efficient estimation of marginal probabilities in statistical physics models.
method Local mappings based on Fourier transform of local factors, applied to Ising, Potts, and clock models.
result Local extrema of fixed points are at phase transition points, and the mapping facilitates efficient estimation.
This work introduces a new metric for comparing imprecise probability models.
problem Quantifying differences between imprecise probability models.
method Integral imprecise probability metric framework based on Choquet integral.
result IIPM enables comparison across different imprecise probability models and quantifies epistemic uncertainty.
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.
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.
Adapts concordance probability for large non-life insurance datasets.
problem Capturing discriminatory ability in large non-life insurance datasets.
method Adapts C-index definition and presents two estimation procedures.
result Validates the new procedures for various versions of C-index.
Generative models improve image probability estimation but lack interpretability.
problem Lack of interpretability in generative models for natural image distributions.
method Extracted explicit probability density estimates from GANs and analyzed latent representations.
result Natural image density functions are difficult to interpret.
Paper simplifies calculating causation probabilities and ranks root causes.
problem Computational challenges in assessing causal relationships.
method Algorithmic simplifications and novel methodological framework for Root Cause Analysis.
result Significantly reduces computational complexity for calculating causation probabilities.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
NNLMs optimize poorly for word probabilities due to embedding space structure.
problem NNLMs assign suboptimal probabilities to some words.
method Analyzed the inductive bias of NNLMs and the structure of word embeddings.
result Words on the convex hull have bounded probability, affecting others.
AI can learn true probabilities if data and assumptions align.
problem Understanding when AI models can accurately represent true objective probabilities.
method Proved conditions under which AI can learn true probabilities.
result Conditions for learning true probabilities are identified.
MPT improves CNN and energy-based models' OOD detection and generalization.
problem Challenging out-of-distribution detection in computer vision.
method Applying Maximum Probability Theorem as a regularization scheme in CNN and energy-based models.
result MPT-based regularization strategy stabilizes and improves generalization and robustness of base models.
This paper analyzes the probability flow in the stock market using the Black-Scholes model.
problem The non-conservation of probability in the stock market.
method Expressed the Black-Scholes equation in Hamiltonian form and analyzed the flow of probability.
result Conditions under which probability might be conserved in the market, challenging the non-Hermitian nature of the Black-Scholes Hamiltonian.
Bayesian model improves win probability estimates in soccer.
problem Technical challenges in estimating win probability for soccer.
method Bayesian statistical framework using contextual game state features.
result Well-calibrated win, tie, and loss probabilities demonstrated.
Bayesian approach to robust risk measures under model uncertainty.
problem Representing robust risk measures as a single probability measure.
method Introducing two types of risk measures and analyzing their relation to robust risk measures.
result Robust risk measures can be represented by a mixture probability measure, a Bayesian approach.
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.
Categorical d-separation criterion simplifies probability graph analysis.
problem Detecting causal relationships in probability distributions.
method Introducing categorical definitions for causal models and d-separation.
result Abstract version of d-separation criterion applies to various probability theories.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.
Two methods estimate rating transition probabilities, one Markov, one non-Markov, differing in default probabilities.
problem Estimating rating transition probabilities and default probabilities accurately.
method Markov and non-Markov frameworks, Fisher information matrix, self-exciting marked point processes.
result Non-Markov model yields higher default probabilities in investment grades, lower in speculative grades.
Investigates statistical properties of perturb-softmax and perturb-argmax distributions.
problem Underexplored statistical properties of Gumbel-Softmax and Gumbel-Argmax distributions.
method Investigates convexity and differentiability to determine completeness and minimality of these distributions.
result Identifies parameters that admit complete and minimal representation of probability distributions.
PSD models simplify probability density estimation.
problem Effective modeling of probability densities for inference.
method Positive semi-definite (PSD) models for non-negative functions.
result PSD models efficiently support product and sum rules.
This paper introduces tools to predict individual survival probabilities across all times.
problem Lack of tools to provide individual survival probabilities across all time points.
method Develops and evaluates new models including extensions to Cox model, Accelerated Failure Time, Random Survival Forests, and Multi-Task Logistic Regression.
result Introduces D-Calibration for evaluating individual survival distribution models.
Sequence probability predicts correctness in LLMs, but not for repeated prompts
problem Predicting correctness in large language models
method Quantifying sequence probability and correctness across different levels
result Higher sequence probability often predicts correctness across prompt-answer pairs
Study AR(1) series for risk model, estimating ruin probability.
problem Estimating ruin probability in risk models with dependent claim numbers.
method Established AR(1) risk model, used Newton iteration method to find adjustment coefficient, estimated ruin probability.
result Developed new method to estimate exponential upper bound of ruin probability.
Study on risk model with claims, dividends, and random probabilities.
problem Analyzing a risk model with claims, delayed claims, and randomized dividends.
method Discrete time Compound Beta-Binomial Risk Model with recursive expressions for Gerber-Shiu function.
result Recursive relations for ruin-related quantities obtained.
Evidential Softmax preserves multimodality in sparse probability distributions for generative models.
problem Sparse probability distributions in deep generative models make exact marginalization computationally intractable.
method Introduce ev-softmax, a sparse normalization function that preserves multimodality and can be trained with probabilistic loss functions.
result ev-softmax outperforms existing techniques in distributional accuracy and dimensionality reduction.
Develops a binomial model in categorical probability spaces.
problem Valuation of financial claims in non-standard filtrations.
method Introduces generalized filtrations in a categorical setting.
result Validates financial claim valuations in new filtrations.
This paper introduces Probability Engineering to improve deep learning models.
problem Challenges in traditional probabilistic modeling for AI applications.
method Treats learned probability distributions as engineering artifacts and actively modifies them.
result Improves robustness, efficiency, adaptability, and trustworthiness of deep learning models.
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.
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.
Proposes an accuracy-preserving calibration method for DNNs.
problem Calibration of deep neural networks (DNNs) to measure prediction reliability.
method Uses Concrete distribution on the probability simplex to calibrate DNNs without accuracy loss.
result The proposed method outperforms previous methods in accuracy-preserving calibration tasks.
Quantum probability metrics improve distribution comparison in high dimensions.
problem Challenges in comparing probability distributions, especially in high-dimensional and non-compact domains.
method Quantum probability metrics (QPMs) derived from quantum state spaces, overcoming limitations of MMD.
result QPMs offer enhanced sensitivity to subtle distributional differences in high dimensions and improve performance in generative modeling.
DoSE improves OOD detection by estimating model probability density.
problem Poor specificity of model likelihoods for OOD detection.
method DoSE uses density of states concept to avoid direct model probability comparison.
result DoSE achieves state-of-the-art performance on OOD detection benchmarks.