We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure, statistical data, and a user's prior knowledge, and returns a score proportional to …
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48 results for “Statistical Prior Assumptions”
Study on GEPs with generative priors, showing optimal statistical rates and proposing an iterative algorithm.
problem Generalized eigenvalue problems with generative priors.
method Assumption of Lipschitz continuous generative model, Projected Rayleigh Flow Method (PRFM).
result PRFM converges linearly to an estimated vector achieving the optimal statistical rate.
New algorithms improve Bayesian linear regression with spike-and-slab priors.
problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.
Optimum-statistical collaboration improves black-box optimization efficiency.
problem Improving black-box optimization efficiency through better statistical collaboration.
method Introducing optimum-statistical collaboration framework for hierarchical bandits-based optimization.
result Demonstrated improved regret bounds and better performance in experiments.
New framework for understanding BSS robustness under model violations.
problem Understanding how BSS solutions behave under statistical prior assumptions violations.
method Introducing an informative topology on the space of possible causes and explicit continuity guarantees.
result First comprehensive robustness framework for BSS.
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past…
New method efficiently evaluates policies using trajectory data.
problem Statistically efficient policy evaluation with limited data.
method Trajectory-based approach for policy evaluation.
result Improved sample complexity for policy evaluation.
Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead …
Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete statistical independence can be too restrictive an assumption in practice. Additiona…
Projected Gradient Descent Algorithms for Solving Nonlinear Inverse Problems with Generative Priorsstat.ML
PGD algorithms solve nonlinear inverse problems with generative priors using noisy measurements.
problem Signal estimation from noisy nonlinear measurements with generative priors.
method Projected gradient descent algorithms for two cases: unknown and known nonlinearity.
result PGD algorithms converge linearly to optimal statistical rates using arbitrary initialization.
A new Weyl prior is proposed for Bayesian statistics, offering a more canonical choice for parameter α.
problem Choosing a prior distribution for Bayesian inference.
method Proposed a new Weyl prior based on the Weyl structure on a statistical manifold.
result The Weyl prior is a special case of the α-parallel prior with α = -n, where n is the dimension of the statistical manifold.
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation. We analyze the algorithm under a new expressivity assumption that we call "optimistic closure," which is strictly weaker than assumptions from prior analyses for the linear setting. With opti…
New method optimizes complex models with minimal data, proving global optimality.
problem Optimizing complex models with unknown cost functions and prior distributions.
method Introduces 'coarse learnability' and an iterative MBO algorithm with sample correction.
result Achieves global optimality with polynomial sample complexity.
Develops methods for constructing likelihoods and priors for Bayesian networks.
problem Learning parameters and structure of Bayesian networks from limited data.
method Introduces assumptions for constructing likelihoods and priors from small assessments.
result Allows construction of likelihoods and priors for a wide range of network structures.
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coe…
Bayesian framework for model uncertainty identifies complex heterogeneity without strong assumptions.
problem Identifying complex heterogeneity in factorial data with varying covariates.
method Rashomon Partition Sets (RPS) using l0 prior for robust model uncertainty.
result RPS provides a robust set of models capturing complex heterogeneity without strong assumptions.
Study proposes learning optimal priors from data for better Bayesian inference.
problem Challenges the use of noninformative uniform priors in Bayesian inference.
method Machine learning approach to learn optimal priors from data using a target function.
result Study models consistently outperformed baseline models in Wikipedia category classification.
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all (potentially suboptimal) classifiers. Our work also justifies assumptions made in prior w…
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques f…
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence for the regularized solution under the prior assumptions and a certai…
Improved bounds for unbounded losses using transductive priors.
problem Sequential regression and classification with unbounded losses.
method Exponential weights algorithm with transductive priors.
result Statistical bounds independent of design vectors and optimal solution norm.
Optimizes exp-concave losses with a new risk bound.
problem Optimizing exp-concave losses with stochastic convex optimization.
method Empirical Risk Minimization with a unified geometric assumption and local norms.
result Provides an excess risk bound.
Statsformer validates and adapts LLM-derived semantic priors for improved supervised learning.
problem Unreliable semantic priors from LLMs can degrade supervised learning performance.
method Adapts LLM-derived feature scores into a family of learner-specific prior-injection mechanisms, calibrating their influence using out-of-fold validation.
result Improves prediction performance by adaptively downweighting unreliable LLM priors, ensuring a guardrailed statistical learning system.
Independent component analysis (ICA) is a widely used BSS method that can uniquely achieve source recovery, subject to only scaling and permutation ambiguities, through the assumption of statistical independence on the part of the latent sources. Independent vector analysis (IVA) extends the applicability of ICA by joi…
New method for distributional off-policy evaluation using Bellman residual minimization.
problem Learning return distribution from offline data generated by a different policy.
method Energy Bellman Residual Minimizer (EBRM) method.
result Established finite-sample error bound for EBRM estimator.
Adversarial consistency depends on the uniqueness of adversarial Bayes classifiers.
problem Consistency of adversarial surrogate losses is not guaranteed.
method Connected consistency of adversarial surrogate losses to the uniqueness of adversarial Bayes classifiers.
result A convex surrogate loss is statistically consistent for adversarial learning if and only if the adversarial Bayes classifier is unique.
"No free lunch" results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling. Some models are expensive (strong assumptions, such as as subgaussian tails), others are cheap (simply finite variance). As it is well known, the more you pay, the…
Empirical Decision Theorystat.ME
Empirical model tackles decision problems without specifying states of the world.
problem Decision problems under uncertainty with inaccessible states of the world.
method Empirical approach using observed act--consequence pairs as model primitives.
result Optimality in empirical decision problems addressed using protocol-based empirical choice functions.
The paper improves bandit algorithms by incorporating random-effect models.
problem Improving statistical efficiency in multi-armed bandit problems with misspecified priors.
method Introduces a random-effect model to bandits, estimating arm means and designing a UCB algorithm ReUCB.
result Derives an upper bound on the Bayes regret of ReUCB, showing improved performance over Thompson sampling.
Scalable PnP-ADMM for large-scale imaging problems.
problem Heavy computational and memory requirements of current PnP algorithms.
method Incremental variant of PnP-ADMM with theoretical convergence guarantees.
result Fast convergence and scalability compared to existing PnP algorithms.
A new probabilistic model for semi-supervised learning unifies various methods.
problem Combining different aspects of data distribution for semi-supervised learning.
method A probabilistic model that interprets and improves upon existing SSL methods.
result The model unifies various SSL methods and extends to neuro-symbolic learning.
A maximum entropy model of bounded rational decision-making with prior beliefs and market feedbackcs.IT
Model captures decision-making under bounded rationality with prior beliefs and market feedback.
problem Bounded rationality in decision-making with limited processing abilities.
method Maximum entropy principle applied to Quantal Response Statistical Equilibrium framework.
result Prior beliefs influence decision-making, altering the outcome of market feedback.
Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributionsstat.ML
Diffusion models learn multi-modal distributions with optimal efficiency.
problem Learning high-dimensional distributions with low-dimensional multi-modal structures.
method Score-based diffusion models, focusing on subgaussian distributions within subspaces.
result Diffusion models require samples for 1-Wasserstein error, improving over prior guarantees.
New methods solve sparse estimation robustly, even with outliers.
problem Sparse estimation in high-dimensional data with outliers.
method Non-convex optimization formulations for robust sparse mean estimation and PCA.
result Any approximate stationary point yields near-optimal solutions.
Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean. This assumption naturally leads to the common choice of a standard Gaussian prior over continuous latent variables. Recent work has, however, shown that this prior has a detrimental ef…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from mean-field variational Bayesian inference. The conditions pertain to the existence of cer…
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error va…
PDGMM-VAE uses adaptive priors for better ICA recovery.
problem Nonlinear ICA recovery of latent source signals.
method Adaptive per-dimension Gaussian mixture model priors in a variational autoencoder.
result PDGMM-VAE effectively recovers source-specific non-Gaussian marginals.
Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another type is generative modelling of signal distributions. Generative models based o…
Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote models using a small subset of regressors. To increase statistical power, the so-c…
We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data , sketching algorithms use a sketching matrix, with $r \…
New algorithm reduces prediction error in online learning without knowing base measure.
problem Smoothed online learning without knowledge of base measure.
method R-Cover algorithm based on recursive coverings.
result First algorithm to guarantee sublinear regret for agnostic smoothed online learning without prior knowledge of base measure.
In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words -- i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the an…
Investor optimizes investment strategy under model uncertainty and random utility.
problem Optimizing investment under model ambiguity and random utility.
method Proves existence of optimal strategy using primal methods, with assumptions on market and utility function.
result Existence of optimal investment strategy proven.
Study phase retrieval under misspecified models using generative priors.
problem Estimating signals from phase measurements with model misspecification.
method Two-step approach: spectral initialization followed by iterative refinement.
result Statistical rate of order under suitable conditions.
Develops a simulation-based method to translate expert knowledge into prior distributions for Bayesian models.
problem Effective incorporation of expert knowledge into prior distributions for diverse model structures.
method Simulation-based stochastic gradient descent to learn hyperparameters of parametric priors from expert knowledge.
result Method is adaptable to various elicitation techniques and independent of model structure.