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.
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.
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.
Variational autoencoders (VAE) have quickly become a central tool in machine learning, applicable to a broad range of data types and latent variable models. By far the most common first step, taken by seminal papers and by core software libraries alike, is to model MNIST data using a deep network parameterizing a Berno…
Gaussian prior and likelihood improve bandit learning performance.
problem Improving bandit learning with misspecified Gaussian distributions.
method An agent with a bounded information ratio interacts with a Bernoulli bandit based on a Gaussian prior and likelihood.
result The regret increase is at most linear in the square-root of the time horizon for diffuse distributions.
New binary AA methods improve on existing techniques.
problem Binary data limitations in AA methods.
method Proposed two optimization frameworks for binary AA.
result Superior performance on synthetic and real binary data.
Maximum likelihood estimator performance in logistic regression analyzed.
problem Performance of maximum likelihood estimator in logistic regression.
method Sharp non-asymptotic guarantees for existence and excess logistic risk.
result Sharp guarantees for the existence and excess risk of MLE in logistic regression.
Innovative game theory approach optimizes survival analysis metrics.
problem Survival analysis models trained with maximum likelihood do not directly optimize criteria like Brier score or Bernoulli log likelihood.
method Inverse-Weighted Survival Games: Construct objectives from re-weighted estimates featuring the other model, holding the latter fixed during training.
result Games optimize Brier score on simulations and real-world data.
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.
New ZIPLN model accounts for zero-inflation in multivariate count data.
problem Zero-inflation in multivariate count data.
method Introduced Zero-Inflated PLN (ZIPLN) model with variational inference.
result ZIPLN significantly improves log-likelihood and reduces dispersion.
Adaptive learning method identifies and corrects corrupted data.
problem Robust learning from corrupted training sets.
method Identifies corrupted and non-corrupted samples with latent Bernoulli variables, formulates as likelihood maximization with marginalized latent variables, solved via variational inference and Expectation-Maximization.
result Improves over state-of-the-art by automatically inferring corruption level with minimal overhead.
CRBMs improve financial regime detection with PCD and free energy analysis.
problem Detecting systemic risk regimes in financial time series.
method Extended RBM to CRBM with autoregressive conditioning and PCD. Decomposed free energy into magnitude and correlation components.
result CRBM's free energy metric distinguishes between magnitude shocks and market regimes.
Self-supervised method improves representation learning for better accuracy.
problem Improving representation learning without manual annotation.
method Proposes a novel self-supervised formulation of relational reasoning.
result Self-supervised relational reasoning outperforms state-of-the-art models by 14% in accuracy.
New model captures insurance risk dependencies efficiently.
problem Dependence modeling in sparse time series of insurance claims.
method Comb-Bernoulli model bridging Lévy copulas and zero-mixed models.
result Model enables tractable simulation, likelihood evaluation, and parameter estimation.
A learning algorithm achieves logarithmic regret in a market making model.
problem Learning the price sensitivity parameter in a market making model.
method Maximum-likelihood estimator with regularization, based on HJB equation.
result Regret upper bound of order ln^2 T in expectation.
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.
We consider a problem of ecological inference, in which individual-level covariates are known, but labeled data is available only at the aggregate level. The intended application is modeling voter preferences in elections. In Rosenman and Viswanathan (2018), we proposed modeling individual voter probabilities via a log…
We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size …
New model for multivariate discrete event data with flexible interactions.
problem Modeling multivariate discrete event data with categorical interactions.
method Developed a new modeling approach with convex constraints, two estimation procedures (LS and ML).
result Proposed model can capture arbitrary shapes of historical event influence.
The expectation-maximization (EM) algorithm has been widely used in minimizing the negative log likelihood (also known as cross entropy) of mixture models. However, little is understood about the goodness of the fixed points it converges to. In this paper, we study the regions where one component is missing in two-comp…
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…
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.
SpinSVAR estimates SVAR models with sparse input, improving accuracy and scalability.
problem Estimating SVAR models with sparse input assumptions.
method SpinSVAR models input as independent Laplacian variables, enforcing sparsity and using least absolute error regression.
result SpinSVAR outperforms state-of-the-art methods in accuracy and runtime, identifying significant structural shocks.
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.
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dynamical systems with …
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard n-dimensional simplex. Under certain conditions, this random walk is self-similar and corresponds …
A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to …
Neural Boltzmann Machines improve on CRBMs for modeling data.
problem Limited expressivity of CRBMs with noisy data.
method Convert CRBM parameters to neural networks.
result NBMs can approximate data likelihood better.
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, …
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.
Conjugate pairs of distributions over infinite dimensional spaces are prominent in statistical learning theory, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much of the existing literature in the learning community focuses on processes posses…
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.
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.
We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate of our posterior update rule to the true probability function in…
Unified CS for GLMs improves bandit regret bounds.
problem Improving regret bounds for GLMs in bandit settings.
method Unified likelihood ratio-based CS with PAC-Bayesian bound.
result Unified CS attains poly(S)-free regret for Bernoulli.
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…
Multivariate Bernoulli autoregressive (BAR) processes model time series of events in which the likelihood of current events is determined by the times and locations of past events. These processes can be used to model nonlinear dynamical systems corresponding to criminal activity, responses of patients to different med…
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. Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with Bernoulli units. Here, we consider an alternative member of exponential family RBM with…
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.
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estima…
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.
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.
Two approaches extend knowledge distillation to Gaussian Processes, showing relationships to existing methods.
problem Applying knowledge distillation to Gaussian Processes for regression and classification.
method Data-centric and distribution-centric approaches to extend distillation to GPR and GPC.
result Distribution-centric approach for GPC approximately corresponds to data duplication and scaling.