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.
Improves A/B testing by detecting minor treatment effects.
problem Challenges in identifying small average treatment effects.
method Maximum probability-driven two-armed bandit (TAB) process with weighted mean volatility statistic.
result Significant improvement in A/B testing with reduced experimental costs.
This paper optimizes Bayesian acquisition functions in Gaussian Processes for better optimization.
problem Improving the efficiency of Bayesian optimization methods.
method Analysis of different acquisition functions and optimizers for optimizing Bayesian acquisition functions.
result Optimization of acquisition functions leads to faster and more accurate sampling points.
New algorithms minimize MMD to approximate probability measures efficiently.
problem Approximating probability measures by representative point sets.
method Sequential greedy minimization of maximum mean discrepancy (MMD) over candidate sets, with mini-batch variants.
result Consistency of proposed algorithms and mini-batch variants established.
Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to sc…
Classifiers based on probabilistic graphical models are very effective. In continuous domains, maximum likelihood is usually used to assess the predictions of those classifiers. When data is scarce, this can easily lead to overfitting. In any probabilistic setting, Bayesian averaging (BA) provides theoretically optimal…
Improves probability distribution compression with KT algorithm.
problem Efficiently compressing probability distributions.
method Kernel thinning (KT) algorithm with four improvements.
result KT yields tighter, dimension-free guarantees for any kernel.
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probabi…
New estimators improve efficiency in two-phase designs with coarsened data.
problem Efficient estimation in two-phase designs with incomplete data.
method Developed new estimators within the TMLE framework.
result New estimators are asymptotically equivalent and more efficient.
Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.
problem Overfitting in maximum likelihood estimation.
method Introduces a regularization approach based on gauge symmetry in Kullback-Leibler divergence.
result The method provides a theoretically guaranteed optimal model without frequent hyperparameter tuning.
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using …
The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.
problem The dependence of maximum a posteriori estimates on parametrization.
method Assuming a Riemannian manifold with Fisher metric, the paper reinterprets priors and posteriors as distributions over probability distributions, making estimates independent of parametrization.
result A maximum a posteriori estimate independent of parametrization is defined.
We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems transforms the search for a probability density into the solution of a differential…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Ma…
MAXENT method outperforms ML in sparse data with specific prior correlations.
problem Evaluating MAXENT method's validity limits and comparing it with ML.
method Bayesian decision theory, Dirichlet density, KL distance, regularized maximum likelihood.
result MAXENT can outperform ML in sparse data with specific prior correlations.
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.
MEP-Net uses MEP to generate solutions from limited data.
problem Generating solutions to scientific problems with incomplete information.
method Combines MEP with neural networks to learn complex distributions from moment constraints.
result Demonstrates MEP-Net's effectiveness in modeling biochemical reaction networks and generating complex distributions.
Optimization of very expensive black-box functions requires utilization of maximum information gathered by the process of optimization. Model Guided Sampling Optimization (MGSO) forms a more robust alternative to Jones' Gaussian-process-based EGO algorithm. Instead of EGO's maximizing expected improvement, the MGSO use…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The most important function is arguably the Euclidean distance between data items, …
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. When the problem is formu…
Probability versions of Li-Yau inequalities for manifolds with boundary.
problem Establishing Li-Yau inequalities for manifolds with non-convex boundaries.
method Stochastic analysis and Bakry-Emery curvature-dimension approach.
result Explicit probability versions of Li-Yau inequalities for manifolds with boundary.
New decision-theoretic calibration error metric improves prediction reliability.
problem Improving the reliability of predictions for decision-making.
method Proposed Calibration Decision Loss (CDL) and an efficient algorithm to achieve near-optimal CDL.
result Near-optimal CDL guarantees vanishing payoff loss from miscalibration.
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…
Improved manifold-adaptive dimension estimator for better data complexity assessment.
problem Estimating intrinsic dimensionality of complex data.
method Revised and improved Farahmand-Szepesvári-Audibert (FSA) estimator, incorporating probability density function and median.
result Median-FSA estimator outperforms existing methods in accuracy and robustness.
Maximizes probability of completing investment schedules with optimal portfolio weights.
problem Optimizing probability of completing investment schedules with optimal portfolio weights.
method Computing maximum probability and optimal portfolio weight functions for various rebalancing schedules.
result Noticeable improvements in probability to complete schedules with optimal portfolio weights.
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
problem Unified understanding of KL-divergence and IPMs.
method Unified representation via maximum likelihood density-ratio estimation (DRE).
result Unified form of IPMs and novel DRM metrics.
New KQEs improve probability metrics without mean function constraints.
problem Improving probability metrics without relying on mean function representations.
method Kernel quantile embeddings (KQEs) to construct new distances.
result KQEs offer a competitive alternative to MMD with near-linear cost.
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
We propose ROI regularization (ROIreg) as a semi-supervised learning method for image classification. ROIreg focuses on the maximum probability of a posterior probability distribution g(x) obtained when inputting an unlabeled data sample x into a convolutional neural network (CNN). ROIreg divides the pixel set of x int…
Efficient algorithms for large Maxent models improve wildfire probability predictions.
problem Training large-scale, non-smooth Maxent models efficiently for big data.
method First-order optimization algorithms using Kullback-Leibler divergence.
result Our algorithms outperform state-of-the-art methods by one order of magnitude.
Quantum ML predicts data with improved speed and accuracy.
problem Predicting data using maximum likelihood in a quantum setting.
method Quantum states embedding and minimization of quantum relative entropy.
result Unified framework for classical and quantum LLMs with performance guarantees.
Generative models improve image restoration from unknown transformations.
problem Restoring images distorted by unknown transformations.
method Combining maximum a-posteriori probability with maximum likelihood estimation.
result Restores images without requiring exact knowledge of transformations.
The paper shows how MMD metrizes weak convergence for certain kernels.
problem Characterizing MMD metrizing weak convergence for a wide class of kernels.
method Proving MMD metrizes weak convergence for specific kernels on a locally compact space.
result Corrected prior results and identified new kernels metrizing weak convergence.
Maximizing withdrawal success in a pooled annuity fund with multiple annuitants.
problem Optimizing withdrawal success in a pooled annuity fund with homogeneous annuitants.
method Maximizing the probability of completing withdrawals until death over portfolio weight functions.
result Increasing the number of annuitants can significantly increase the maximum probability of withdrawal success.
New method estimates Schrödinger bridges using ML techniques.
problem Finding most likely stochastic evolution between two distributions.
method Equivalence with maximum likelihood estimation, numerical Gaussian process approach.
result Direct application of ML techniques for SBP estimation.
Deep Reinforcement Learning improves with Weighted Q-Learning to reduce bias and uncertainty.
problem Overestimation and high variance in Q-Learning cause learning algorithms to diverge in complex environments.
method Deep Weighted Q-Learning (Deep WQL) uses Dropout and Monte Carlo sampling to approximate WQL's weights and reduce bias.
result Deep WQL reduces bias and improves performance on benchmarks compared to existing methods.
Developed R package for creating nomograms for any ML algorithms.
problem Creating nomograms for any machine learning algorithms.
method Formulated a function to transform ML prediction models into nomograms, requiring specific datasets.
result Created 5 types of nomograms for various ML algorithms and predictor types.
The paper proposes a new probability distribution for rooted trees.
problem Overfitting in tree selection for statistical models.
method Bayesian approach with a generalized probability distribution for rooted trees.
result Recursive methods to evaluate the probability distribution without approximations.
New causal versions of MaxEnt and PIR avoid paradoxical probability updates.
problem Paradoxical probability updates in causal MaxEnt and PIR.
method Separate constraints into cause-specific and mechanism-specific restrictions.
result Causal MaxEnt avoids paradoxical updates and aligns with Information Geometric Causal Inference.
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.
Given i.i.d. observations of a random vector X∈Rp, we study the problem of estimating both its covariance matrix Σ∗, and its inverse covariance or concentration matrix {Θ∗=(Σ∗)−1.} We estimate Θ∗ by minimizing an ℓ1-penalized log-determinant Bregman divergence; in the multivariate G…
Paper uses stats to predict treatment choice based on illness probability.
problem Improving treatment decision-making in personalized medicine.
method Statistical decision theory with maximum regret evaluation.
result Estimates illness probability for better treatment choice.
New framework improves experimental design using integral probability metrics.
problem Challenges in Bayesian Optimal Experimental Design (BOED) with KL divergence.
method Integrates integral probability metrics (IPMs) for stability and flexibility.
result IPM-based designs yield more robust and accurate credible sets.
M-flows learn data manifolds and densities, improving manifold learning and inference.
problem Representing datasets with manifold structure more faithfully.
method Combining normalizing flows, GANs, autoencoders, and energy-based models, with a new training algorithm.
result M-flows learn data manifolds better than standard flows and provide handles for dimensionality reduction.
Reduces quantifier variance with accuracy optimization of base classifier.
problem Minimizing quantifier variance under prior probability shift.
method Optimizes the Brier score of a base classifier for training data.
result Optimizing Brier score on training data reduces quantifier variance on test data.
Paper improves likelihood estimation for discrete distributions.
problem Computing profile maximum likelihood for discrete distributions.
method New bounds on Bethe and Sinkhorn permanents for low rank matrices.
result Achieves an approximation factor of exp(-O(sqrt(n) log n)) in polynomial time.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double sided HMM. This makes it possible to use ergodic theorems. As an applicatio…