The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
New approach to neural networks by incorporating observation noise and arbitrary prior means.
problem Misspecification on noisy data and limitations of NTK-GP equivalence.
method Introducing a regularizer for observation noise and proposing a shifted network for arbitrary prior means.
result Removes key obstacles to practical Gaussian process modeling in neural networks.
New priors for deep neural networks converge to Gaussian processes.
problem Improving the performance and stability of deep neural networks.
method Extending prior distributions to include non-zero means and partially exchangeable priors, leading to a new Gaussian process model.
result The new Gaussian process model avoids pathologies and improves performance on regression problems.
When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge from data acquired in related tasks. When it comes to meta-learning in Gaussian…
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Paper proposes a method to break symmetries in Bayesian matrix factorization.
problem Symmetries in posterior distribution reduce MCMC sampling efficiency.
method Modification to Gaussian prior mean and covariance to break symmetries.
result Breaking symmetries leads to lower autocorrelation and reconstruction errors.
Study shows prior Lipschitz continuity can improve adversarial robustness of Bayesian Neural Networks.
problem Improving adversarial robustness of Bayesian Neural Networks.
method Analysis of i.i.d., zero-mean Gaussian priors and posteriors approximated via mean-field variational inference.
result Adversarial robustness is sensitive to the prior variance.
Additive Bayesian networks are types of graphical models that extend the usual Bayesian generalized linear model to multiple dependent variables through the factorisation of the joint probability distribution of the underlying variables. When fitting an ABN model, the choice of the prior of the parameters is of crucial…
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…
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.
We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertain…
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
CW-Gen models improve probabilistic time series forecasting by incorporating prior information.
problem Challenges in probabilistic forecasting of multivariate time series due to non-stationarity, inter-variable dependencies, and distribution shifts.
method CW-Gen framework that incorporates prior information through conditional whitening. JMCE learns conditional mean and covariance, improving sample quality.
result CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches.
New meta-reinforcement learning method improves performance in finite-horizon MDPs.
problem Improving meta-reinforcement learning in finite-horizon MDPs with shared optimal action-value functions.
method Proposes MTSRL and MTSRL+ algorithms with learned priors and covariance, coupled with prior-alignment technique for meta-regret guarantees.
result Achieves meta-regret guarantees with learned priors and covariance, outperforming prior-independent RL and bandit-only meta-baselines.
New method uses quotient predictor space for better PAC-Bayes bounds, reducing KL divergence and improving model performance.
problem Overparameterized models with continuous symmetries can lead to biased predictions.
method Perform PAC-Bayesian analysis on quotient predictor space, constructing a canonical prior that reflects model's implicit bias.
result The new prior reduces KL divergence and improves model performance in experiments.
Bayes-assisted confidence sequences improve efficiency for bounded means.
problem Efficient uncertainty quantification for bounded IID means without parametric assumptions.
method Bayesian working predictive model selects adaptive martingale updates maximizing predictive log-growth.
result Asymptotically log-optimal performance with informative priors reducing width and sampling effort.
Flexible Bayesian approach for generalized linear models, especially for sparse logistic regression.
problem Sparse logistic regression challenges in machine learning.
method Empirical Bayes approach with mean-field variational inference, tuning-free and scalable.
result Superior predictive performance in sparse logistic regression compared to existing methods.
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
problem Handling hyperparameters for non-informative limits in multivariate Gaussian conjugate priors.
method Using scaled KL-divergence between multivariate Gaussians to construct Wishart and normal-Wishart conjugate priors.
result Forming non-informative priors without violating Wishart shape parameter restrictions.
Wide BNNs with odd activations fail to approximate data under mean-field inference.
problem Theoretical limitations of mean-field variational inference in wide, deep Bayesian neural networks.
method Analysis of mean-field variational inference in fully-connected BNNs with odd activation functions and Gaussian likelihood.
result The optimal mean-field variational posterior predictive distribution converges to the prior predictive distribution as network width increases.
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…
New insights into empirical Bayes and compound decision problems with improved regret bounds.
problem Estimating means of normally or Poisson distributed vectors under squared loss.
method Combines Bayesian and frequentist approaches using data-driven estimators.
result Optimal regret bounds for Poisson and normal mean models, resolving conjectures.
The explore{exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning is intractable. Planning with the mean MDP is a common myopic approxi…
The choice of sentence encoder architecture reflects assumptions about how a sentence's meaning is composed from its constituent words. We examine the contribution of these architectures by holding them randomly initialised and fixed, effectively treating them as as hand-crafted language priors, and evaluating the resu…
The concept of sample mean in dynamic time warping (DTW) spaces has been successfully applied to improve pattern recognition systems and generalize centroid-based clustering algorithms. Its existence has neither been proved nor challenged. This article presents sufficient conditions for existence of a sample mean in DT…
A method for converting NIW parameters for better estimation.
problem Estimating parameters of multivariate normal distribution.
method Convergent procedure for converting mean parameters to natural parameters in NIW family.
result Maximum likelihood estimation of natural parameters from observed statistics.
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².
Exemplar-based clustering methods have been shown to produce state-of-the-art results on a number of synthetic and real-world clustering problems. They are appealing because they offer computational benefits over latent-mean models and can handle arbitrary pairwise similarity measures between data points. However, when…
We consider the stochastic multi-armed bandit problem with a prior distribution on the reward distributions. We are interested in studying prior-free and prior-dependent regret bounds, very much in the same spirit as the usual distribution-free and distribution-dependent bounds for the non-Bayesian stochastic bandit. B…
New GP kernels avoid mean reversion without losing smoothness.
problem Pathological behavior in stationary GP regression.
method Improper Gaussian processes with non-positive kernels.
result Stationary, non-reverting covariance functions.
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless …
Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based on undecimated wavelet transform and an iterative image reconstruction algorith…
We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…
Adversarial meta-learning computes Gamma-minimax estimators for vague prior knowledge.
problem Estimating parameters with vague prior knowledge.
method Adversarial meta-learning algorithms for Gamma-minimax estimators.
result Convergence guarantees and neural network class for selection.
In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution of a product of two normally distributed variables with zero means and possibly …
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.
IAGAN method improves medical image reconstruction by incorporating adaptive GAN priors.
problem Reconstructing high-fidelity medical images from incomplete data.
method Image-adaptive GAN-based reconstruction method (IAGAN).
result IAGAN can recover fine structures relevant for medical diagnosis.
New algorithm clusters data with almost-linear time, robust to corruption.
problem Clustering mixtures of distributions with adversarial corruption.
method List-decodable mean estimation, robust mean estimation, iterative multi-filtering.
result First almost-linear time algorithms for clustering mixtures of k well-behaved distributions.
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,…
Thompson sampling has impressive empirical performance for many multi-armed bandit problems. But current algorithms for Thompson sampling only work for the case of conjugate priors since these algorithms require to infer the posterior, which is often computationally intractable when the prior is not conjugate. In this …
Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in netw…
Bayesian framework for sphere regression using Gaussian fields.
problem Nonparametric regression on the sphere with Gaussian priors.
method Isotropic Gaussian field priors, harmonic structure, exact posterior distributions, optimal spectral truncation, posterior contraction rates.
result Sharp posterior contraction rates for Gaussian priors with polynomially decaying angular power spectra.
Study Nash equilibrium in market with relative wealth concerns under partial information and heterogeneous priors.
problem Analyzing Nash equilibrium in a market with unobservable return rates and heterogeneous priors.
method Established a Nash equilibrium through a separation result and martingale argument. Used fully-coupled linear FBSDEs and deep neural networks for numerical computation.
result Investment strategies under relative wealth concerns exhibit a herd effect, with accurate prior estimators leading the market.
New data-dependent priors improve PAC-Bayes bounds.
problem Improving PAC-Bayes bounds for nonconvex learning.
method Using data to learn a conditional expectation of the posterior, given a subset of training data.
result Data-dependent oracle priors lead to stronger PAC-Bayes bounds.
Proposes I-prior extension for additive interaction models.
problem Challenges in estimating and selecting models with interactions.
method Extends I-prior methodology to multiple covariates, introducing a parsimonious model specification.
result Improves estimation and model selection for additive interaction models.
Deep Gaussian Processes with polynomial kernels can collapse rapidly without proper hyperparameter tuning.
problem The collapse of Deep Gaussian Processes with polynomial kernels without careful hyperparameter tuning.
method Analysis using the Berry-Esseen Theorem and observation of prior behavior.
result The prior of a Deep Gaussian Process collapses rapidly towards zero or places negligible mass on low norm functions without proper hyperparameter tuning.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
Proposes a method to quantify uncertainty in PFNs.
problem Lack of uncertainty quantification in PFNs.
method Martingale posteriors for efficient, tuning-free sampling.
result Proves convergence of proposed sampling procedure.