New definition of MCVaR for discrete probability spaces.
problem Existing definitions of MCVaR not suitable for discrete random variables.
method Proposes vector-valued MCVaR (VMCVaR) for discrete probability spaces.
result VMCVaR provides advantages over existing definitions for discrete cases.
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 calculates tail probabilities of random vectors under linear transformations.
problem Computing tail probabilities of random vectors under linear transformations.
method Characterization of regular variation on cones in [0,∞)d under random linear transformations. result Allows computation of probabilities of tail events that were previously negligible.
Support vector machines have attracted much attention in theoretical and in applied statistics. Main topics of recent interest are consistency, learning rates and robustness. In this article, it is shown that support vector machines are qualitatively robust. Since support vector machines can be represented by a functio…
A new method for comparing image probability measures using convolution operators.
problem Efficiently comparing images using conventional sliced Wasserstein methods.
method Proposed convolution sliced Wasserstein (CSW) methods with stride, dilation, and non-linear activation.
result CSW demonstrates favorable performance over conventional sliced Wasserstein in image comparison and deep generative modeling.
Support vector classifier constructs confidence sets for binary classification.
problem Learning confidence sets with specific probability guarantees for binary classification.
method Support vector classifier to construct confidence sets.
result The proposed learner controls non-coverage rates and minimizes ambiguity with high probability.
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.
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.
Study identifies partitions of probability distributions using multi-armed bandits.
problem Identifying the correct partition of a vector of probability distributions.
method Developed sample complexity bounds and proposed algorithms for multi-armed bandit settings.
result Characterized lower bounds on mean number of samples and proposed algorithms matching these bounds.
Numbers and numerical vectors account for a large portion of data. However, recently the amount of string data generated has increased dramatically. Consequently, classifying string data is a common problem in many fields. The most widely used approach to this problem is to convert strings into numerical vectors using …
Proposes novel wSVMs for sparse learning and accurate probability estimation.
problem Sparse features with redundant noise limit the performance of existing wSVMs.
method Develops ℓ1-norm and elastic net regularized wSVMs for automatic variable selection and probability estimation. result Elastic net regularized wSVMs achieve superior performance in variable selection and probability estimation.
In this paper we propose a simple yet powerful method for learning representations in supervised learning scenarios where each original input datapoint is described by a set of vectors and their associated outputs may be given by soft labels indicating, for example, class probabilities. We represent an input datapoint …
Paper tackles one-bit compressed sensing using PAC learning theory.
problem One-bit compressed sensing problem.
method Formulated as PAC learning problem, uses VC-dimension and PAC learning theory.
result Consistent algorithm can recover k-sparse vectors with O(klg(n/k)) measurements. A new approach to MI learning using bag-to-class divergence.
problem Sparse MI training sets and difficulty in classifying bags.
method Introducing bag-to-class divergence to MI learning, emphasizing hierarchical random vectors.
result Bag-to-class divergence is a more effective classifier for MI learning.
Paper analyzes proper losses and their performance in machine learning tasks.
problem Understanding the performance of estimators and forecasters in machine learning tasks.
method Analyzes surrogate regret and convergence rates for strictly proper losses.
result Strongly proper losses achieve the optimal convergence rate.
A new machine learning method calculates failure probability efficiently and accurately.
problem Computing the probability of failure for complex systems.
method Penalized Profile Support Vector Machine with adaptive sampling and clustering.
result The method minimizes model evaluations while preserving decision boundary geometry.
New method improves feasibility of fitting Gaussian vectors to an ellipsoid.
problem Feasibility of fitting n Gaussian vectors to an ellipsoid boundary. method Improved concentration of Gram matrices using Bartl & Mendelson (2022) results.
result Feasibility of (P) with high probability when n≤d2/C. The paper establishes concentration bounds for embeddings of generative models.
problem Analyzing statistical properties of generative models.
method High probability concentration bounds on sample vector embeddings using Data Kernel Perspective Space.
result Determines the number of samples needed for accurate approximation of generative model embeddings.
RVFL networks can efficiently approximate Lipschitz functions in L∞ norm.
problem Efficiently approximating Lipschitz continuous functions in L∞ norm.
method Random Vector Functional Link (RVFL) network with ReLU activation functions, proving approximation in L∞ norm.
result An RVFL with ReLU activation functions can approximate Lipschitz continuous functions in L∞ norm.
New linear algorithms improve wSVMs for multiclass probability estimation.
problem Estimating conditional probabilities for multiclass problems.
method Proposed baseline learning and OVA learning schemes to improve wSVMs.
result Linear algorithms achieve optimal computational efficiency and good estimation accuracy.
Some high-dimensional data.sets can be modelled by assuming that there are many different linear constraints, each of which is Frequently Approximately Satisfied (FAS) by the data. The probability of a data vector under the model is then proportional to the product of the probabilities of its constraint violations. We …
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.
The study shows how to accurately estimate embedding vectors in high dimensions.
problem How to accurately estimate embedding vectors in high-dimensional spaces.
method A simple probability model and a variant of low-rank approximate message passing (AMP) method.
result The AMP approach enables precise predictions of the accuracy of the estimation in certain high-dimensional limits.
Active covariance estimation using random sub-sampling of variable subsets.
problem Estimating covariance matrices for partially observed random vectors.
method Unbiased covariance estimator under a model of partially observed variables and active learning framework.
result Derivation of error bounds revealing relations between sub-sampling probabilities and covariance matrix entries.
Estimates mean of random vector with near-optimal error in all directions.
problem Estimating the mean of a random vector with direction-dependent accuracy.
method Proves existence of an estimator with near-optimal error in all directions under certain conditions.
result The estimator satisfies the error bound for all directions, with probability 1-δ.
Study spectral properties of sparse random graphs to recover latent vectors.
problem Recovering latent vectors in sparse random geometric graphs.
method Analyzes spectral concentration and uses orthogonal polynomial expansions, decoupling, and matrix concentration.
result Sharpens spectral norm bounds and proves exact recovery for Gaussian mixture models.
Generalizes Barankin bound for vector cases in mean square error.
problem Achieving the lower bound of mean square error for vector estimates.
method Finite dimensional vector Riesz representation theorem and linear matrix inequality.
result Necessary and sufficient conditions for achieving the lower bound.
A theorem divides hyperplanes evenly with a line through the origin.
problem Dividing hyperplanes evenly with a line.
method Direct proof using measures on hyperplanes.
result A line through the origin divides hyperplanes evenly.
Develops a new approach for detecting context-dependent multivariate outliers.
problem Challenges of detecting context-dependent multivariate outliers.
method Transforms conditional detection to unconditional space and uses classifier chain decomposition.
result Methodology successfully identifies outliers in sparse or dense conditions.
New algorithm recovers vectors from quadratic equations with high probability.
problem Recovering unknown vectors from quadratic equations with random measurements.
method Truncated Amplitude Flow (TAF) algorithm, two-stage approach.
result TAF recovers the solution exactly with high probability and linear complexity.
LITE efficiently estimates Gaussian PoM with linear time and memory complexity.
problem Estimating the probability of maximality (PoM) of Gaussian vectors efficiently.
method LITE: entropy-regularized UCB approach for almost-linear time and memory complexity.
result Achieves state-of-the-art accuracy with significantly faster performance than existing methods.
New model for online ranking with feature analysis.
problem Online ranking with click probability and feature vectors.
method Linear function of feature vector and unknown parameter; novel algorithm with improved regret.
result Improved algorithm handling large number of items with reduced dependence on item count.
Proposes deep learning methods for handling random vectors.
problem Handling flexible input data like probability measures in deep learning.
method Develops deep architectures to handle permutation invariances, varying weights, and cardinality.
result Demonstrates the effectiveness of deep architectures on measures for classification, reduction, and prediction.
Let X be a data matrix of rank ρ, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We pr…
Statistical method recognizes driving styles using vehicle speed and throttle opening.
problem Recognizing driving styles for improved vehicle performance and safety.
method Bayesian probability and kernel density estimation to describe driving styles uncertainty.
result Classifies driving styles into seven levels based on vehicle speed and throttle opening.
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
problem Handling statistical surrogates for stochastic manifolds with heterogeneous data.
method A transient anisotropic kernel is introduced to improve statistical surrogates for stochastic manifolds with heterogeneous data.
result The transient anisotropic kernel provides a better representation of statistical dependencies in the learned probability measure.
The paper develops a theory of surplus invariance in vector lattices.
problem The role of surplus invariance in risk measures and capital requirements.
method The development of surplus invariance in vector lattices.
result Dual representations and extensions of surplus-invariant risk measures.
Efficient learning of minimax risk classifiers in high dimensions.
problem Efficient learning of classifiers in high-dimensional data.
method Iterative algorithm leveraging constraint generation methods for minimax risk classifiers.
result The algorithm provides efficient learning and feature selection in high-dimensional scenarios.
Study curvature of infinite dimensional manifold of Hölder equilibrium probabilities.
problem Analyzing curvature of infinite-dimensional manifold of Hölder equilibrium probabilities.
method Using Riemannian metric, Ruelle operator, and asymptotic variance to describe curvature.
result Explicit expressions for curvature of orthonormal basis vectors are derived.
Approximates measures on curved spaces using Dirac measures.
problem Topology of invariant measures on curved manifolds.
method Introducing weakly regular vectors and approximating measures by Dirac measures.
result Ergodicity is a generic property in the space of invariant measures supported on weakly regular vectors.
Model predicts enactment probability of U.S. bills using word vectors and context.
problem Predicting the enactment probability of U.S. bills.
method Ensemble model combining text and context variables, using word vectors.
result Combining text and context variables improves prediction accuracy.
New algorithm uses machine learning to predict high-frequency trading returns.
problem Improving prediction accuracy in high-frequency trading.
method Iterative optimization and activation functions in deep learning, combined with VPIN, GARCH, and SVM. result The model significantly improved prediction of market liquidity and trading returns.
Random square-tiled surfaces have normal genus distribution and cover all integer vectors.
problem Distribution and properties of random square-tiled surfaces.
method Randomizing model and local central limit theorem for genus.
result The distribution of the genus is asymptotically normal and contains all primitive integer vectors.
New method AM learns optimal vector fields for entire distribution sequences, matching OT.
problem Optimal Transport (OT) problem in generative modeling.
method Action Matching (AM) method learns optimal vector fields for a sequence of distributions.
result AM method achieves optimal transport by learning vector fields for entire distribution sequences.
We develop a unified approach for classification and regression support vector machines for data subject to right censoring. We provide finite sample bounds on the generalization error of the algorithm, prove risk consistency for a wide class of probability measures, and study the associated learning rates. We apply th…
The paper improves SVR with linear constraints for better model properties.
problem Improving Support Vector Regression with linear constraints.
method Generalized SMO algorithm for solving optimization with linear constraints.
result The proposed method shows better practical performance on various datasets.
AOLS improves sparse linear regression with lower costs and better recovery.
problem Inferring sparse vectors from random linear combinations.
method Accelerated Orthogonal Least-Squares (AOLS) algorithm.
result AOLS achieves lower sampling complexity and better recovery probability.
FFM generates functions between Gaussian and data distributions.
problem Generating functions between Gaussian and data distributions.
method Define a path of measures, learn a vector field to generate this path.
result FFM outperforms other function-space generative models.