Proposes using equivariant generative models for compressed sensing with unknown orientations.
problem Recovering signals with unknown orientations from underdetermined systems of linear measurements.
method Equivariant variational autoencoder as a generative prior for compressed sensing.
result Signals with unknown orientations can be recovered using iterative gradient descent on the latent space of equivariant models.
Bayesian neural networks' performance varies with prior choice, affecting their ability to identify unknowns.
problem The impact of prior choice on Bayesian neural networks' ability to identify unknowns.
method Evaluation of different prior distributions on classification tasks using BNNs and NNs with Monte Carlo dropout.
result Prior choice significantly impacts BNNs' ability to identify unknowns, affecting true and false positive rates.
Proposes PE-GP-UCB for time-varying Bayesian optimisation.
problem Time-varying Gaussian process bandits with unknown prior.
method PE-GP-UCB algorithm, relying on consistency of function values with priors.
result Regret bound provided for the proposed algorithm.
We study the problem of learning shared structure \emph{across} a sequence of dynamic pricing experiments for related products. We consider a practical formulation where the unknown demand parameters for each product come from an unknown distribution (prior) that is shared across products. We then propose a meta dynami…
Thompson sampling used for linear bandits with normal-gamma priors.
problem Optimizing decisions in uncertain environments with linear dependencies and unknown parameters.
method Bayesian Thompson sampling with multivariate normal-gamma priors.
result Derivation of a Bayesian regret bound for the approach.
Advanced and effective collaborative filtering methods based on explicit feedback assume that unknown ratings do not follow the same model as the observed ones (\emph{not missing at random}). In this work, we build on this assumption, and introduce a novel dynamic matrix factorization framework that allows to set an ex…
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
MetaTS learns to explore better by meta-learning prior from bandit instances.
problem Efficient exploration in bandit problems.
method MetaThompson Sampling (MetaTS) that meta-learns the prior from bandit instances.
result MetaTS quickly adapts to unknown prior and achieves better exploration.
Bayesian framework integrates prior and data knowledge for nonlinear dynamical systems.
problem Fusing diverse prior knowledge with data for accurate model learning.
method General-purpose Bayesian inference and learning framework combining explicit and implicit prior knowledge.
result Efficient parameter marginalization and closed-form densities for online and offline inference.
Unrolled networks learn optimal Bayesian inference for unknown priors.
problem Optimizing Bayesian inference when the prior is unknown.
method Unrolling neural networks to simulate iterations of inference algorithms.
result Unrolled networks approximate convergence to optimal denoisers for product priors.
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussi…
Method learns SDEs from one trajectory using GP priors and randomized cross-validation.
problem Learning SDEs from a single trajectory.
method Combining CGC and data-adapted kernels learned via randomized cross-validation.
result Efficacy, robustness, and scope of the method demonstrated in numerical experiments.
Two algorithms improve GP bandits by selecting priors and minimizing regret.
problem Selecting appropriate GP priors for unknown functions.
method Developed two algorithms: Prior-Elimination GP-TS and HyperPrior GP-TS.
result Established sublinear regret bound for HyperPrior GP-TS.
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
problem Understanding the assumptions and dependencies in Bayesian hierarchical models.
method Demonstrates how canonical distributions and maximum entropy principles can be used to derive marginal priors in hierarchical models.
result Marginal priors in hierarchical models derived from maximum entropy principles have different constraints compared to the original priors.
Proposes a learned Bayesian Cramér-Rao bound for unknown measurement models.
problem Computing the Bayesian Cramér-Rao bound requires full knowledge of priors and measurement distributions.
method Introduces a Physics-encoded score neural network to learn priors and measurements.
result Demonstrates improved sample complexity and interpretability through domain knowledge incorporation.
The paper deals with learning probability distributions of observed data by artificial neural networks. We suggest a so-called gradient conjugate prior (GCP) update appropriate for neural networks, which is a modification of the classical Bayesian update for conjugate priors. We establish a connection between the gradi…
Proposes NUV priors for half-space and box constraints.
problem Adding constraints to linear Gaussian models without computational cost.
method Introduces NUV representations for half-space and box constraints.
result Adds constraints to linear Gaussian models without affecting computational tractability.
MAXENT method outperforms ML in sparse data with specific prior correlations.
problem Evaluating MAXENT method's validity limits and comparing it with ML.
method Bayesian decision theory, Dirichlet density, KL distance, regularized maximum likelihood.
result MAXENT can outperform ML in sparse data with specific prior correlations.
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
Paper develops PAC-Bayes bounds for unknown linear systems.
problem Learning controllers for unknown stochastic linear discrete-time systems.
method PAC-Bayes framework for data-dependent high probability bounds.
result Proposes efficient learning algorithms with theoretical guarantees.
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a…
Bayesian method mitigates negative transfer in unknown source data.
problem Negative transfer in transfer learning where target performance worsens after source data consideration.
method Proxy-informed robust method for probabilistic transfer learning (PROMPT).
result Negative transfer can be mitigated without prior knowledge of source data.
Over the past decades, researchers and ML practitioners have come up with better and better ways to build, understand and improve the quality of ML models, but mostly under the key assumption that the training data is distributed identically to the testing data. In many real-world applications, however, some potential …
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.
This paper learns prior models from indirect data efficiently.
problem Learning prior models from indirect data in Bayesian inversion.
method Generative model of prior as pushforward of Gaussian in latent space, learned by minimizing loss function.
result Efficient residual-based neural operator approximation for forward model learning.
Bayesian approach uses deep learning for seismic imaging and uncertainty quantification.
problem Uncertainty in seismic imaging due to nonuniqueness and noise.
method Implicit structured prior from randomly initialized convolutional neural network, combined with Bayesian model averaging and stochastic gradient Langevin dynamics.
result Deep priors reduce imaging artifacts and overfitting in noisy conditions.
A new prior for VAEs improves model capacity by allowing a more flexible latent space.
problem Standard Gaussian priors in VAEs limit model capacity and performance.
method Proposed a Riemannian Brownian motion prior over a Riemannian structure of the latent space.
result The new prior significantly increases model capacity with only one additional scalar parameter.
A new method for accurately reconstructing signals without knowing the kernel or signal regularity.
problem Recovering signals from noisy measurements without prior knowledge of the convolution kernel or signal regularity.
method Parametrizing the convolution kernel and prior length-scales, jointly estimated in the inversion procedure.
result Accurate reconstructions of signals with varying regularity and unknown kernel size.
Identifies root causes of outliers in unknown cyclic graphs.
problem Outliers in unknown cyclic graphs with linear structural equations.
method Identifies a short list of potential root causes based on strong perturbation and structural equations.
result The shortlist includes true root causes and their parents on the cycle.
Solving inverse problems continues to be a central challenge in computer vision. Existing techniques either explicitly construct an inverse mapping using prior knowledge about the corruption, or learn the inverse directly using a large collection of examples. However, in practice, the nature of corruption may be unknow…
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
problem Estimating eigenvectors with small eigen-gap and fine-grained statistical reasoning.
method Eigen-decomposition of asymmetric data matrix, distribution-free procedures, adaptive to heteroscedastic noise.
result Minimax optimal under Gaussian noise, confidence intervals for eigenvalues, small eigen-gap handling.
In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
One of the key challenges in applying reinforcement learning to real-life problems is that the amount of train-and-error required to learn a good policy increases drastically as the task becomes complex. One potential solution to this problem is to combine reinforcement learning with automated symbol planning and utili…
Bayesian neural network achieves nearly optimal performance in Besov space.
problem Bayesian neural networks in Besov space.
method Spike-and-slab prior and shrinkage prior for posterior convergence rate.
result The posterior convergence rate is nearly minimax and adaptive to unknown smoothness.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
Weak diffusion priors can still perform well in inverse problems.
problem Using mismatched or low-fidelity diffusion priors in inverse problems.
method Extensive experiments and theoretical analysis combining Bayesian-consistency theory and local-correlation analysis.
result Weak priors succeed when measurements are highly informative, and they fail in other regimes.
The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult,…
Optimality of TS with noninformative priors proven for Pareto model.
problem Optimality of Thompson Sampling with noninformative priors for Pareto bandits.
method Proved optimality of TS with certain probability matching priors, showed suboptimality with others, and found effectiveness of truncation procedures.
result TS with certain probability matching priors achieves optimal regret bound for Pareto model.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowl…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for in…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for in…
DS-TS adapts to abrupt and smooth changes in bandit problems.
problem Non-stationary multi-armed bandit problems with abrupt and smooth changes.
method Discounted Thompson Sampling with Gaussian priors.
result Achieves nearly optimal regret bound for both abrupt and smooth changes.
Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing a class of nonparametric covariance regression models, which allow an unknown p …
Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.
problem Signal recovery from generative priors in compressed sensing.
method Stochastic Gradient Langevin Dynamics (SGLD) for signal recovery.
result SGLD converges to the true signal under mild assumptions on the generative model.
In this paper we study the problem of recovering a structured but unknown parameter θ∗ from n nonlinear observations of the form yi=f(⟨xi,θ∗⟩) for i=1,2,…,n. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when…