We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…
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48 results for “family approach”
In this paper, we give proofs of the family index formula and the equivariant family index formula by the Greiner's approach to heat kernel asymptotics. We compute equivariant family JLO characters. We also define the equivariant eta form and give a proof of its regularity.
Efficient method for learning continuous exponential families beyond Gaussian.
problem Learning continuous exponential families with unbounded support.
method Interaction Screening approach for scalable learning of continuous graphical models.
result Our estimator maintains similar accuracy and sample complexity scalings compared to alternative approaches, while improving run-time.
Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component parameters, usually the component covariance (or scale) matrices, are decompose…
Hybrid system matches patients with family doctors based on trust and history.
problem Matching patients with suitable family doctors in primary care.
method Hybrid recommender system combining patient trust from consultation histories and temporal dynamics.
result Predictive accuracy is higher than heuristic and collaborative filtering approaches, and trust measure improves performance.
Chentsov's theorem proved for exponential families.
problem Characterizing the Fisher information metric in exponential families.
method Unified proof using the central limit theorem.
result Fisher information metric is the only Riemannian metric invariant under extensions and sufficient statistics.
ASVI automates variational inference for complex models.
problem Efficient variational inference for complex probabilistic models.
method Automatic structured variational inference (ASVI) using convex updates.
result ASVI outperforms other methods on a wide range of problems.
New approach to proving Chen-Donaldson-Sun theorem with examples.
problem Proving Chen-Donaldson-Sun theorem for families of curves.
method Construction of a special metric on stable vector bundles over surfaces formed by families of curves.
result Demonstrates existence of a special metric related to one-dimensional cycles in moduli space.
Generalized Spectral Kernelsstat.ML
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…
New DP framework using data truncation for efficient estimation.
problem Differential privacy in unbounded data support.
method Data truncation, exponential family distributions, maximum likelihood estimation, DP stochastic gradient descent.
result Near-optimal sample complexity for Gaussian mean and covariance estimation.
MulDef defends neural networks against adversarial examples by combining multiple models.
problem Vulnerability of neural networks to adversarial examples.
method A general defense framework based on multiple models with robustness diversity.
result Substantially improved accuracy on adversarial examples (22-74%) while maintaining similar accuracy on legitimate examples.
Study extends binary omniprediction to multiclass setting with improved sample complexity.
problem Suboptimality bounds for each loss function against infinite comparator family in multiclass prediction.
method Design of a framework for solving Blackwell approachability problems with coupled actions.
result Sample complexity of for -omniprediction in a -class problem.
Researchers create a family of solitons connecting a cigar to a sphere.
problem Classifying steady gradient Ricci-Yang-Mills solitons on surfaces.
method Constructed a 1-parameter family of solitons on surfaces.
result Any complete steady gradient Ricci-Yang-Mills soliton on a surface must come from this family.
Study the Lyapunov exponent in SL(2,C) families as parameters approach poles.
problem Understanding the asymptotic behavior of Lyapunov exponents in meromorphic families of matrices.
method Analyzing the blow-up of Lyapunov exponent and relating it to non-Archimedean Lyapunov exponent.
result The blow-up of Lyapunov exponent is governed by a quantity interpretable as the non-Archimedean Lyapunov exponent.
Kernel conditional exponential family generalizes conditional distributions.
problem Modeling conditional distributions with flexibility and consistency.
method Introduces a nonparametric family using RKHS and functional parameters, with an algorithm for learning the natural parameter.
result Consistency of the estimator in well-specified cases, and superior performance in experiments.
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows one to work without introducing ad hoc spaces, by using the language of differe…
Geodesic curves improve flexibility in covariance estimation.
problem Inflexible covariance families limit spatiotemporal modeling.
method Use geodesic curves to build more flexible covariance families.
result Natural projection minimizes geodesic distance to sample covariance.
We show that if a Legendrian knot in standard contact ${\bb R}^3$ possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology (LCH) is isomorphic to singular homology groups arising from the generating family. In this setting we show …
A new VSMC family improves variational inference efficiency and accuracy.
problem Efficient and accurate Bayesian inference for complex models.
method Integrates variational inference and sequential Monte Carlo for flexible posterior approximation.
result VSMC family can approximate posterior arbitrarily well and optimize parameters efficiently.
New approach for neural models to be transparent over structured data.
problem Training neural models to be transparent in a functional manner.
method Setup as a cooperative game between a predictor and witnesses, encouraging local agreement.
result The predictor remains globally powerful while agreeing locally with witnesses.
Constructing exponential families from statistical manifolds.
problem The central problem of constructing exponential families from statistical manifolds.
method Constructive approach proving every compact statistical manifold admits a foliation of Hessian manifolds.
result Compact orientable leaves are either finite quotients of flat torus or mapping torus with periodic monodromy.
Directional Decision Listsstat.ML
In this paper we introduce a novel family of decision lists consisting of highly interpretable models which can be learned efficiently in a greedy manner. The defining property is that all rules are oriented in the same direction. Particular examples of this family are decision lists with monotonically decreasing (or i…
Study uses Lagrangian approach to prove limiting absorption principle on Riemannian spaces.
problem Proving limiting absorption principle on Riemannian scattering spaces.
method Lagrangian perspective applied to Riemannian scattering spaces.
result Spectral family is Fredholm in function spaces encoding Lagrangian regularity.
An efficient algorithm for Riemannian logarithm on Stiefel manifold family.
problem Efficient computation of Riemannian logarithm on Stiefel manifold for various metrics.
method Generalizes a matrix-algebraic approach for the canonical metric to a one-parameter family of metrics.
result Conserves local linear convergence for the family of metrics.
We investigate minimal surfaces passing a given curve in . Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface. Also we derive the parametric representation of two minimal surface families passing a circle and a helix as examples.
A new method for non-negative matrix factorization using generalized dual divergence.
problem Non-negative matrix factorization for various noise structures.
method Theoretical framework based on generalized dual Kullback-Leibler divergence, with algorithms developed and proven convergence using Expectation-Maximization.
result Generalizes existing methods and provides an alternative for non-negative matrix factorizations.
Paper proves one observation suffices for Gaussian embedding.
problem Proving theoretical underpinnings for Gaussian embedding.
method Developed first theoretical results for exponential family embedding models.
result Learned embedding structure from one observation.
New approach to Generalized Beta family using SDEs.
problem Understanding the Generalized Beta family of distributions.
method Using a mean-reverting SDE for a power of the variable, leading to a modified GB distribution.
result Provides alternative forms and cumulative distribution functions for GB distributions.
The paper calculates indices for families of Fredholm operators and their extensions.
problem Calculating indices for families of Fredholm operators and their extensions.
method Passing from a Fredholm operator to its graph, deforming the horizontal subspace.
result Index formulas for families of Fredholm realizations and self-adjoint extensions.
Constructs instantons on a specific G_2-manifold limit.
problem Finding instantons on a particular G_2-manifold limit.
method Dynamical systems approach involving perturbations of abelian and cone solutions.
result Obtains a 1-parameter family of SU(2) instantons with bounded curvature.
Geometrically revisits Dupin cyclidic systems using evolving circles and cyclides.
problem Understanding the geometric properties and evolution of Dupin cyclidic systems.
method Evolving initial circles or Dupin cyclides to generate Lamé families of Dupin cyclidic systems in various space forms.
result Lamé families are parallel surfaces in different space forms.
We study the problem of finding the smallest such that every element of an exponential family can be written as a mixture of elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding th…
New method uses neural exponential families for likelihood-free inference.
problem Bayesian Likelihood-Free Inference with intractable likelihood.
method Score Matching neural conditional exponential families for approximate likelihood.
result State-of-the-art performance in posterior sampling for intractable likelihood models.
Estimates exponential family distributions using a novel doubly dual embedding technique.
problem Estimating exponential family distributions with smoothness and efficiency.
method Doubly dual embedding for avoiding partition function computation and flexible sampling.
result Improves memory and time efficiency while offering stronger statistical properties.
Bayesian approach generalizes ADMM for federated learning.
problem Improving federated learning efficiency and accuracy.
method Integrates Bayesian duality with ADMM for optimization.
result New extensions of ADMM for various distributions.
This paper analyzes VAE approximation errors in conditional exponential families.
problem Posterior collapse and approximation errors in VAEs.
method Analysis of ELBO objective and conditional exponential families.
result The ELBO optimizer pulls away from the likelihood optimizer towards a consistent subset of models.
The paper proves left-orderability for certain Dehn fillings of pseudo-Anosov mapping tori.
problem Left-orderability of fundamental groups in Dehn fillings of pseudo-Anosov mapping tori.
method Two approaches: one using -covered foliations and the other using one-sided branching.
result All such Dehn fillings have left-orderable fundamental groups.
A new clustering algorithm inspired by Wittgenstein's philosophy.
problem Clustering data without assuming predefined cluster shapes or sizes.
method Wittgenstein's family resemblance concept applied to machine learning.
result WFR clustering algorithm effectively identifies clusters in data.
Extends likelihood ratio exponential families to analyze various optimization methods.
problem Analyzing optimization methods like rate-distortion and information bottleneck.
method Linking geometric mixture paths to exponential families and using hypothesis testing.
result Provides a common mathematical framework for understanding these methods.
A deep learning approach for fitting complex distributions.
problem Limited applicability of simple kernels in fitting complex distributions.
method Learning a deep network to parameterize the kernel of the exponential family.
result The method can fit complex structures on moderate-dimensional problems.
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…
Extends topological theorems to new mapping families.
problem Limitations of existing topological theorems.
method Replaces large subset requirements with smaller subset requirements.
result Extends theorems to m-sphere to n-space mappings with m<n.
Boosting improves data fitting while maintaining fairness guarantees.
problem Ensuring fairness in data preprocessing.
method Boosting algorithm to learn sufficient statistics of exponential families.
result The learned distribution maintains fairness guarantees while fitting the data better.
Proves stability of Schwarzschild black holes without symmetry assumptions.
problem Stability of Schwarzschild black holes under general conditions.
method Teleologically normalised double null gauges, analysis of linear stability, and control of non-linearities.
result Proves non-linear asymptotic stability of Schwarzschild family as solutions to Einstein vacuum equations.
Using Takahashi theorem we propose an approach to extend known families of minimal tori in spheres. As an example, the well-known two-parametric family of Lawson tau-surfaces including tori and Klein bottles is extended to a three-parametric family of tori and Klein bottles minimally immersed in spheres. Extremal spect…
We study conformal -subgeometry of submanifolds in a semi-Riemannian -manifold, focusing on conformal -manifolds and their Poincaré-Einstein metrics . Our approach is based on the spectral theory of Dirac operator in the ambient -manifold, and associated spinor valued meromorp…
A new method for selecting high quality itemsets from a large collection.
problem Selecting a small, high-quality subset of patterns from a larger collection of itemsets.
method Using decomposable families of itemsets and a junction tree structure.
result The method provides high quality results and is computationally efficient.
New algorithm for efficiently identifying the best arm in stochastic bandits.
problem Best arm identification in stochastic multi-armed bandits with fixed confidence.
method Sequential probability ratio tests for arm selection.
result Asymptotically optimal sample complexity and guaranteed PAC performance.