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.
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.
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…
Estimates parameters of high-dimensional Bernoulli autoregressive process with long-range dependence.
problem Estimating parameters of a multivariate Bernoulli process with auto-regressive feedback in high dimensions.
method Proposes and analyzes an ℓ 1 \ell_1 ℓ 1 -regularized maximum likelihood estimator (MLE) under the assumption of approximate sparsity. result Derives precise upper bounds on mean-squared estimation error.
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…
Critical trajectories in a sphere are found for a specific bending functional.
problem Finding closed trajectories in a sphere for a specific bending functional.
method Existence of infinitely many closed trajectories shown for a given Lagrange multiplier.
result Existence of closed trajectories dependent on a pair of relatively prime natural numbers.
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.
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.
Study of closed trajectories in hyperbolic plane with specific curvature constraints.
problem Critical trajectories in hyperbolic plane for a specific energy function.
method Classification of critical trajectories based on momentum causal character, proof of existence of closed trajectories.
result Existence of countably many closed trajectories with time-like momentum.
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.
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.
Paper confirms Feldman's conjecture on two-armed bandit problem.
problem Two-armed bandit problem with general distributions and utility functions.
method Obtained necessary and sufficient condition for myopic strategy optimality.
result Myopic strategy stochastically maximizes wins in Bernoulli bandit problems.
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.
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.
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…
A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.
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.
Bayesian optimization for binomial outputs with multifidelity.
problem Optimizing functions with binomial outputs that don't fit Gaussian process assumptions.
method General Gaussian process model for binomial data, Expected Improvement acquisition function, heuristic sample selection.
result Improves optimization performance for binomial target functions.
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.
This work tackles community recovery in hypergraphs with measurements of varying sizes.
problem Cluster data points into distinct communities based on measurements with varying sizes.
method Characterizes the fundamental limits on the number of measurements required for community reconstruction in hypergraphs with homogeneity and parity measurements, possibly corrupted by noise.
result Characterizes fundamental limits on the number of measurements required for community reconstruction in hypergraphs.
Study phase transitions in identifying infected individuals using group testing.
problem Identifying a set of k infected individuals from a population using pooled tests.
method Two random assignment designs (constant-column and Bernoulli) and polynomial-time inference procedures.
result Sharp phase transitions in statistical and computational limits for detection and recovery problems.
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.
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.
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 l 1 l_1 l 1 -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, …
GLR-klUCB detects change-points in non-stationary bandits efficiently.
problem Non-stationary bandit problems with piecewise stationary behavior.
method Combines kl-UCB with a changepoint detector based on GLR.
result Achieves O ( T A Υ T log ( T ) ) O(\sqrt{TA Υ_T\log(T)}) O ( T A Υ T log ( T ) ) regret for some instances. 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 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.
The paper extends consistency results for sequential design strategies to vector-valued Gaussian processes.
problem Estimating excursion sets of vector-valued Gaussian processes.
method Clarifying the connection between continuous Gaussian processes and Gaussian measures in Banach spaces, extending concepts and properties from scalar-valued settings to vector-valued settings.
result Consistency results for sequential design strategies can be applied to vector-valued Gaussian processes.
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.
New Gibbs sampling reduces GLMB filtering complexity to linear time.
problem NP-hard GLMB density computation in multi-object systems.
method Tempered Gibbs sampler exploiting GLMB structure.
result Linear complexity O ( T ( P + M ) ) \mathcal{O}(T(P+M)) O ( T ( P + M )) for GLMB filtering. 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.
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.
This research simplifies computation of feature attribution methods under certain conditions.
problem Computational complexity of feature attribution methods, especially power indices.
method Identifying conditions for polynomial computation and introducing new indices.
result Conditions for efficient computation of feature attribution methods are identified.
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.
New algorithm minimizes regret in stochastic linear bandits with perturbed history.
problem Minimizing cumulative regret in stochastic linear bandits.
method Perturbed-history exploration in a linear bandit (LinPHE) algorithm.
result Achieves a O ( d n ) O(d \sqrt{n}) O ( d n ) gap-free bound on cumulative regret. The paper analyzes how employers can efficiently screen candidates using multiple tests, considering both skill estimation and fairness.
problem How to efficiently screen candidates using multiple noisy signals without violating fairness.
method The paper extends traditional screening models to a multi-test setting, analyzing optimal employer policies for both fixed and dynamic test assignments.
result A fundamental impossibility emerges when noise levels vary across groups, making it impossible to administer the same number of tests and maintain the same outcomes.
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.
New L L L -functions for 3-manifolds connect to Witten invariants and relate to generalized Bernoulli polynomials.
problem Understanding L L 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 L 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.
GDF approach compared to cross-validation for AICc in machine learning models.
problem Estimating model complexity for machine learning models, especially for binary data.
method Generalised Degrees of Freedom (GDF) for model sensitivity, compared to cross-validation.
result GDF-based AICc is similar to cross-validation but unstable for binary data.
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 ( log p ) O(\log p) O ( log p ) . 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.