Study shows flows with maximal entropy are either Bernoulli or a product of a Bernoulli and rotational flow.
problem Characterizing ergodic measures of maximal entropy for smooth flows.
method Analyzes the structure of ergodic measures of maximal entropy for smooth three-dimensional flows.
result Smooth flows with maximal entropy are either Bernoulli or a product of a Bernoulli and rotational flow.
We solve Euler equations on graph manifolds, classifying steady flows with Morse-Bott Bernoulli functions.
problem Classifying steady Euler flows with Morse-Bott Bernoulli functions.
method Constructing non-vanishing steady solutions using integrable systems and topology.
result Steady Euler flows with Morse-Bott Bernoulli functions exist only on graph three-manifolds.
The paper finds unique equilibrium states for geodesic flows on certain surfaces.
problem Analyzing geodesic flows on surfaces without focal points.
method Proving the existence of unique equilibrium states for specific potentials.
result There are unique equilibrium states for certain potentials, including geometric multiples of scalar less than 1.
We prove that the geodesic flow for the Weil-Petersson metric on the moduli space of Riemann surfaces is ergodic (in fact Bernoulli) and has finite, positive metric entropy.
New techniques analyze steady fluid flows on non-compact manifolds.
problem Analyzing steady fluid flows on non-compact manifolds with cylindrical ends.
method New techniques using b-calculus and b-symplectic structures. result New proofs and descriptions of b-symplectic structures on singular sets of the Bernoulli function. Compact support steady flow in 3D Euler equations found.
problem Finding a nontrivial steady Euler flow with compact support.
method Constructing a nontrivial smooth steady incompressible Euler flow in three dimensions with compact support.
result A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support constructed.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
problem Understanding minimal dependence among Bernoulli random vectors.
method Geometric and algebraic representations of multivariate symmetric Bernoulli distributions.
result Characterizes extremal negative dependence and builds minimal dependence copulas.
Upper bound on expected supremum of Bernoulli process.
problem Bounding the supremum of Bernoulli processes.
method Using properties of the index set and function class, extending earlier results on Gaussian processes.
result An upper bound on the expected supremum of a Bernoulli process.
Simple algorithm approximates rare event frequencies.
problem Approximating the frequency of rare events.
method Iterative update of categorical click-distribution, resulting in a random walk on an n-dimensional simplex.
result The random walk corresponds to a biased Bernoulli convolution under certain conditions.
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can e…
The study counts geodesics on special manifolds without focusing points.
problem Counting geodesics on specific types of manifolds.
method Margulis-type asymptotic estimates and analysis of geodesic flow.
result The geodesic flow on these manifolds has a unique measure of maximal entropy with the Bernoulli property.
Finite index solutions to Bernoulli problem are always axially symmetric.
problem Entire solutions to the Bernoulli free boundary problem with finite Morse index in 3D.
method Proof of axial symmetry for finite index solutions.
result Finite index solutions to the Bernoulli problem in 3D are axially symmetric.
Algorithm learns smooth probability functions from Bernoulli tests with guarantees.
problem Learning smooth probability functions from Bernoulli tests with contextual features.
method Scalable algorithm with rigorous L2-norm convergence guarantees for posterior update rule.
result Empirical convergence rates match theoretical guarantees, superior to state-of-the-art.
Let S be a nonexceptional oriented surface of finite type. We construct an uncountable family of probability measures on the space of area on holomorphic quadratic differentials over the moduli space for S containing the usual Lebesgue measure. These measures are invariant under the Teichmueller geodesic flow, and they…
Proves a principle for one-phase Bernoulli problem minimizers.
problem One-phase Bernoulli problem minimizers.
method Strong maximum principle, Alt-Caffarelli functional, Hardt-Simon-type foliation.
result Constructs a foliation for global minimizers.
A new distribution fixes a common error in VAEs, improving image quality.
problem Using a Bernoulli likelihood for pixel data in VAEs.
method Introducing the continuous Bernoulli distribution.
result The continuous Bernoulli improves image quality across various metrics and datasets.
New formula for Bernoulli numbers linking algebra and topology.
problem Explicit formula for Bernoulli numbers and their properties.
method Analytic and algebraic proofs, involving a function in two variables and topological self-intersections.
result A generalized Kronecker formula for Bernoulli numbers with applications in topology.
Model quantifies market price of trading liquidity risk and market depth.
problem Analyzing the market price of trading liquidity risk and market depth.
method Introduced a framework to analyze market price of liquidity risk, derived inhomogeneous Bernoulli ODE, obtained closed form solutions.
result Market depth encapsulates the market price of liquidity risk.
Bayesian autoencoders improve OOD detection by addressing Bernoulli likelihood issues.
problem Out-of-distribution (OOD) detection fails with Bernoulli likelihood for certain datasets.
method Proposes Bayesian autoencoders and alternative likelihood models to fix the issue.
result Bayesian autoencoders and alternative likelihood models improve OOD detection accuracy.
This paper proposed a new regression model called l1-regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a Bernoulli process, this paper also presented a Bernoulli estimate model which, …
Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.
problem Analyzing quasimorphisms on negatively curved spaces.
method Thermodynamic formalism framework, Banach isomorphism, weak Livšic cohomology.
result Establishes Central Limit Theorem and invariance principle for unbounded quasimorphisms.
The paper cleans label noise in supervised classification using Bernoulli sampling.
problem Label noise degrades supervised classifier performance.
method Proposes a label noise cleaning method based on Bernoulli random sampling.
result The method separates clean and noisy observations without prior label information.
This paper tackles open problem of tight bounds for KBs with Bernoulli rewards.
problem Open problem of tight bounds for Kernelized Bandits with Bernoulli rewards.
method Focus on Bernoulli model, not subgaussian noise, and optimize function in RKHS.
result Open problem remains unsolved in this context.
Dasgupta and Shulman showed that a two-round variant of the EM algorithm can learn mixture of Gaussian distributions with near optimal precision with high probability if the Gaussian distributions are well separated and if the dimension is sufficiently high. In this paper, we generalize their theory to learning mixture…
Spectral method speeds fitting of binary time series models.
problem Modeling binary time series data with latent linear dynamical systems.
method Spectral learning of probit-Bernoulli latent linear dynamical systems.
result Spectral method provides robust, fixed-cost estimator.
Paper justifies ST estimator using pWGF and proposes an improved variant.
problem Theoretical justification for ST estimator for discrete variables.
method Interpreted ST as pWGF simulation and proposed an improved estimator.
result Established theoretical foundation for ST estimator and improved variant.
A new method for efficient nonlinear process monitoring using random Bernoulli features.
problem High computational demands and real-time responsiveness in online monitoring systems.
method Random Bernoulli principal component analysis to capture nonlinear patterns efficiently.
result The proposed methods offer excellent scalability and reduced computational complexity.
Proposes a new method for feature selection in non-linear functions.
problem Feature selection for non-linear functions in high-dimensional data.
method Continuous relaxation of Bernoulli distributions to learn feature selection indicators via gradient descent.
result Demonstrates the effectiveness of the approach on synthetic and real-life applications.
Tensorial description of Turaev cobracket for genus 0 surfaces.
problem No specific problem stated; describes a mathematical object.
method Group-like expansion and use of Bernoulli numbers.
result Tensorial description of Turaev cobracket on genus 0 compact surfaces.
A new method uses Mean Field Games to optimize mixture models of Bernoulli and categorical distributions.
problem Optimizing parameters of finite mixture models of Bernoulli and categorical distributions.
method Mean Field Games theory applied to multi-population systems.
result The Mean Field Games approach provides a method to compute mixture model parameters.
A new algorithm resamples Bernoulli race particle filters using true weights.
problem Handling intractable weights in particle filters.
method Proposes a novel resampling method using true weights with an unbiased estimator.
result Demonstrates lower variance in filtering estimates compared to standard methods.
First order invariants of generic immersions of manifolds of dimension nm-1 into manifolds of dimension n(m+1)-1, m,n>1 are constructed using the geometry of self-intersections. The range of one of these invariants is related to Bernoulli numbers. As by-products some geometrically defined invariants of regular homotopy…
New L-functions for 3-manifolds connect to Witten invariants and relate to generalized Bernoulli polynomials.
problem Understanding L-functions for 3-manifolds and their invariants. method Using Mellin transforms and asymptotic techniques, proving entire functions and their values.
result Linear relations between L-function values at negative integers, generalizing known zeta functions. Improved regret bounds for DP-KLUCB and DP-IMED in Bernoulli bandits.
problem Minimizing regret in stochastic bandits under ε-global Differential Privacy.
method Developed DP versions of KLUCB and IMED, proving tighter lower bounds and matching upper bounds.
result DP-KLUCB and DP-IMED achieve asymptotically optimal regret under ε-global DP.
Adaptive network sparsification improves model compactness and accuracy.
problem Suboptimal network sparsification due to input-independent dropout.
method Dependent variational beta-Bernoulli dropout.
result Significantly more compact networks with consistent accuracy improvements.
Paper compares credit portfolio risks using robust Bernoulli mixture models.
problem Tackles risk bounds and comparison of credit portfolio losses.
method Uses Bernoulli mixture models with conditional independence and stochastic increasing defaults.
result Provides conditions for comparing conditional default probabilities and portfolio losses.
We introduce BAR processes for modeling binary interactions and show they mix rapidly.
problem Modeling binary interactions in various graphical structures.
method Introduce Bernoulli Autoregressive Processes (BAR) with autoregressive dynamics and efficient structure learning.
result BAR processes mix rapidly with a mixing time of O(logp). New acquisition functions improve Bernoulli LSE.
problem Efficiently estimating regions where a Bernoulli function is above or below a threshold.
method Developed new look-ahead acquisition functions for Gaussian process classification models.
result Demonstrated clear benefits of new acquisition functions on benchmark and real-world tasks.
A new framework predicts links in time-dependent networks using Bernoulli autoregression.
problem Predicting links in time-dependent networks with additional auxiliary information.
method A Bernoulli autoregressive model with regularization for link discovery.
result The model can discover new links not present in the data.
The paper proves ML estimators are strongly consistent for identifying edge weights in BAR models.
problem Identifying edge weights in Bernoulli Autoregressive (BAR) models.
method Maximum Likelihood (ML) estimation for two variants of BAR models.
result ML estimators are strongly consistent for edge weight identification.
BeMF improves recommendation reliability in recommender systems.
problem Improving reliability in recommender systems beyond accuracy.
method Bernoulli Matrix Factorization (BeMF) for model-based collaborative filtering.
result BeMF selects more reliable predictions, improving recommendation quality.
Study analyzes symmetric two-armed Bernoulli bandit problem with zero mean gap.
problem Analyzing symmetric two-armed Bernoulli bandit problem with zero mean gap.
method Associated with a solution of a linear heat equation, compute leading order terms of minmax optimal regret and pseudoregret.
result Explicitly compute leading order terms in three scaling regimes for the gap.
Exact simulation of correlated binary outcomes using PMF constraints and linear programming.
problem Simulating dependent Bernoulli outcomes with specific means and correlations.
method Formulate the problem over the joint Bernoulli PMF, impose constraints, and solve as a linear program. Use convex-hull characterization and truncated-moment completion scheme for feasibility and simulation.
result Exact simulation framework for correlated binary outcomes, providing a convex-hull characterization and truncated-moment completion scheme.
A new sampling method balances multi-label datasets by preserving category frequency order.
problem Sampling challenges in multi-label datasets with varying label frequencies.
method Uses multivariate Bernoulli distribution and label dependencies to estimate and weight label combinations.
result Produces a more balanced sub-sample with enhanced representation of minority categories.
A new RBM model handles both linear and log-amplitude spectrograms.
problem Handling amplitude spectra with existing models.
method Proposed gamma-Bernoulli RBM that uses gamma distribution.
result The model can naturally handle positive numbers and log-amplitude spectrograms.
Paper analyzes conditions for clustering BMMs with unknown clusters.
problem Clustering Bernoulli Mixture Models (BMMs) with unknown number of clusters.
method Theoretical analysis of sample complexity and dimensionality for PAC-clusterability.
result First non-asymptotic bounds on sample complexity for learning or clustering BMMs.
Proposes a non-parametric method for deep discrete latent variable models.
problem Learning sparse discrete latent representations in deep models.
method Iterative algorithm with Beta-Bernoulli process prior and local data scaling.
result Improves sparsity and scalability of deep discrete latent variable models.
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …