Paper improves tree probability estimation using stochastic optimization and variance reduction.
problem Improving tree probability estimation in phylogenetic inference.
method Introduces computationally efficient methods for training SBNs and variance reduction for optimization.
result Methods outperform previous baseline methods in tree topology probability estimation and Bayesian phylogenetic inference.
Paper explores how risk-averse individuals' willingness to pay for insurance varies with risk probability.
problem Understanding how risk-averse individuals' willingness to pay for insurance varies with risk probability.
method Analyzes willingness to pay (WTP) for partial risk reduction within the dual theory of decision.
result In dual theory, reducing the probability of risk and providing insurance can be complementary if the surplus increases with risk reduction.
The paper provides statistical guarantees for generative models using dimension reduction.
problem Improving the quality of generative models without increasing dimensionality.
method Modeling generative devices as smooth transformations of a lower-dimensional space and using integral probability metrics.
result Established a risk bound showing the impact of dimension reduction on generative model error.
Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain …
Explains SNE, t-SNE, and their variants for manifold learning.
problem Dimensionality reduction and manifold learning.
method Probabilistic approach using Gaussian and Student-t distributions.
result Out-of-sample extension and acceleration methods for t-SNE.
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these method…
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
SQFA learns features maximizing Fisher-Rao distance for better classification.
problem Improving classification accuracy through feature learning.
method SQFA learns linear features maximizing Fisher-Rao distance between class-conditional distributions.
result SQFA-H features achieve the best classification accuracy.
Maximal Rate of Stepwise Uncertainty Reduction selects simulations to reduce uncertainty efficiently.
problem Efficiently estimating quantities of interest from multi-fidelity simulations.
method Bayesian sequential strategy that maximizes the ratio of expected uncertainty reduction to simulation cost.
result MR-SUR strategy unifies and provides principled approaches to develop new methods.
Enhances MOT with causality constraints for better option pricing.
problem Limited applicability of traditional martingale optimal transport (MOT) for option pricing.
method Integrates causality constraints into MOT and proposes McCormick relaxations for computational tractability.
result Empirically, McCormick MOT yields significant price reductions for basket and digital options compared to classic MOT.
Proposes rounding method for precise treatment effect estimation under budget constraints.
problem Resource-constrained experimental design for precise treatment effect estimation.
method Dependent randomized rounding procedure to convert assignment probabilities into binary treatment decisions.
result Improved estimator precision through variance reduction and efficient inference.
Wassmap reduces image complexity while preserving key features.
problem Global nonlinear dimensionality reduction in imaging.
method Wassmap uses Wasserstein space and pairwise distances to create isometric embeddings.
result Wassmap can recover parameters of image manifolds like translations and dilations.
A new method using energy distance for ensemble and scenario reduction.
problem Solving complex dynamic and stochastic programs, especially in energy systems.
method Proposes a new method based on energy distance for ensemble and scenario reduction.
result Reduced scenario sets exhibit better statistical properties for energy distance than Wasserstein distance.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
Paper extends MLFD to signed measures via bilevel approach.
problem Risk minimization for infinite width neural networks and sparse deconvolution.
method Bilevel reduction to extend MLFD to signed measures, investigating convergence rates.
result Improved convergence rates for bilevel MFLD in low-noise regime and local exponential convergence for single neuron learning.
Mathematical analysis of SNE and t-SNE for dimension reduction.
problem Optimal mapping of high-dimensional data to low dimensions.
method Gradient flow of relative entropy to minimize the distance between points.
result The diameter of the evolving sets remains bounded for SNE but may blow up for t-SNE.
Given a Kähler manifold (Z,J,ω) and a compact real submanifold M⊂Z, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group G on the space of probability measures on M. In particular, we prove convexity results for such map when G is A…
Bayesian method for estimating inputs leading to specific probability outputs.
problem Estimating inputs for specific probability outputs of uncertain functions.
method Bayesian strategy using Gaussian process modeling and SUR principle.
result Surpassed performance of existing methods through numerical experiments.
The paper optimizes distribution estimation with high probability in Kullback-Leibler divergence.
problem Estimating discrete distributions with high probability in Kullback-Leibler divergence.
method Uses online learning techniques for novel estimator construction via online-to-batch conversion.
result Optimal rate of estimation is pinned down up to a doubly logarithmic factor of K.
PosCal training improves classification models by calibrating posterior probabilities.
problem Poorly calibrated posterior probabilities in classification models.
method End-to-end training procedure that directly optimizes the objective while minimizing the difference between predicted and empirical posterior probabilities.
result PosCal training achieves about 2.5% task performance gain and 16.1% calibration error reduction.
Reduces complexity of financial contagion dynamics on networks.
problem Complexity of financial contagion dynamics on networks.
method Dimensional reduction methods (degree-weighted and spectral reduction).
result Spectral reduction better handles heterogeneous networks.
Modified relative universality for unbiasedness and consistency in dimension reduction.
problem Gap in proof of unbiasedness and Fisher consistency in relative universality.
method Modified definition of relative universality using ǫ-measurability.
result Established unbiasedness and Fisher consistency rigorously.
Novel unsupervised feature selection method using multi-step Markov transition probability.
problem Neglected relationships between non-adjacent data points in feature selection.
method MMFS (Multi-step Markov transition probability for Feature Selection) approach, employing positive and negative viewpoints.
result MMFS effectively maintains data structure in unsupervised feature selection.
Two new estimators reduce costs and improve accuracy for EHR outcome prediction.
problem Sparse estimate distributions, high computational cost, and high sampling variance in EHR outcome prediction.
method Proposed SCOPE and REACH estimators that leverage next-token probability distributions.
result SCOPE and REACH match Monte Carlo accuracy with token reductions of 2.5-3.4 times and variance guarantees.
This work examines consistency issues in Gaussian Mixture Model reduction algorithms.
problem Consistency issues in Gaussian Mixture Model reduction algorithms.
method Discussion of the importance of dissimilarity measure choice and consistency of GMR algorithms.
result Most existing GMR algorithms are not consistent with a unique measure, leading to suboptimal reduced GMs.
Nonparametric adaptive robust control tackles model uncertainty in stochastic processes.
problem Model uncertainty in stochastic processes.
method Adaptive robust control methodology using online learning and uncertainty reduction, empirical distribution, and Lagrangian duality.
result Nonparametric adaptive robust control approach is preferable to traditional robust frameworks.
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and…
The problem of quantile hedging for basket derivatives in the Black-Scholes model with correlation is considered. Explicit formulas for the probability maximizing function and the cost reduction function are derived. Applicability of the results for the widely traded derivatives as digital, quantos, outperformance and …
A deep learning method for probabilistic weather forecasting.
problem Probabilistic forecasting of weather.
method Two chained machine-learning steps: dimension reduction and density estimation using normalizing flows.
result The method produces accurate conditional forecast distributions for weather.
Paper improves efficiency in matrix computations for Gaussian processes.
problem Efficiency in matrix computations for Gaussian processes.
method Variance reduction via matrix factorization.
result Factorized estimator can be up to 1,000 times more efficient.
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous daughter nodes according to a split point that maximizes the reduction in sum of …
This paper simplifies finding least favorable priors by reducing dimensionality.
problem Finding least favorable priors is challenging due to infinite-dimensional optimization.
method Develops a dimensionality reduction method using Bregman divergences.
result Allows use of gradient ascent algorithms for finding least favorable priors.
PPI uses predictions and weighting to infer from partially labeled data.
problem Valid inference with partially labeled data.
method Combines model-based predictions with bias correction from labeled data, using Horvitz-Thompson and Hájek corrections.
result IPW-adjusted PPI with estimated propensities performs similarly to known-probability case.
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantag…
Direct approach for handling contextual bandits with latent state dynamics.
problem Handling contextual bandits with latent state dynamics, especially when rewards depend on posterior probabilities of hidden states.
method Direct reduction to standard linear contextual bandits, extended analysis of HMM parameters, periodic update of reward-model parameters.
result Periodic update of reward-model parameters allows handling complex dependencies in hidden states.
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification, motivated by the dual of the Kantorovitch problem. Among the algorithms we consi…
We consider the problem of estimating the conditional probability of a label in time O(log n), where n is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Mot…
Reduces false positives in classifying rare online platforms.
problem Challenges in accurately identifying rare online platforms with ML.
method Calibrated probabilities and ensembles to reduce bias.
result Significantly reduces false positives in rare event detection.
The paper analyzes how to combine self-protection and self-insurance for risk reduction.
problem Combining self-protection and self-insurance for risk reduction when market insurance is absent.
method The approach uses Value-at-Risk and Tail Value-at-Risk to evaluate residual risk and solves the problem using isoquant geometry based on marginal-balance curves.
result The analysis identifies the conditions under which self-protection and self-insurance behave as substitutes or complements.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
NoiseRank reduces label noise without supervision, improving classification accuracy.
problem Label noise in datasets from noisy channels.
method NoiseRank uses Markov Random Fields to estimate and rank instances based on their noise probability.
result NoiseRank improves classification accuracy on noisy datasets.
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
New method improves scalability of SGD for large datasets.
problem High variance in stochastic gradient descent.
method Adaptive measure reduction with Carathéodory's theorem.
result Improved scalability to high-dimensional spaces.
This paper optimizes binary linear classifiers by tuning their weight vectors.
problem Optimizing the weight vector of binary linear classifiers for better performance.
method Parameterization of the discriminant through a scalar to control trade-offs between informative and noisy terms.
result Weight vector tuning compensates for non-optimal native hyperparameters, improving classification performance.
Unified probabilistic foundation for fuzzy simplicial sets in dimensionality reduction.
problem Lack of clear probabilistic interpretation in fuzzy simplicial sets.
method Introducing a probabilistic framework explaining fuzzy simplicial sets as marginals of probability measures on simplicial sets.
result Unified probabilistic theoretical foundation for fuzzy simplicial sets.
We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no pa…