Sharp asymptotics derived for phase retrieval and compressed sensing with random generative priors.
problem Phase retrieval and compressed sensing with random measurement matrices.
method Sharp asymptotics derived for optimal performance and polynomial algorithm for random generative priors.
result Compressed phase retrieval becomes tractable with random generative priors, unlike sparse priors.
Study characterizes training and test risks for MAP regression with Gaussian priors.
problem Understanding high-dimensional behavior of regularized linear regression with informative priors.
method Maximum a posteriori (MAP) regression with Gaussian priors, using random matrix theory.
result Closed-form risk formulas reveal the bias-variance-prior tradeoff and explain double descent.
RP-WNO extends WNO with uncertainty quantification, useful for scientists and engineers.
problem Uncertainty in predictions of deep learning models.
method Randomized Prior Wavelet Neural Operator (RP-WNO) with uncertainty quantification module.
result RP-WNO effectively estimates uncertainty in predictions.
Adds a randomized prior network to improve uncertainty in deep reinforcement learning.
problem Improving uncertainty estimation for sequential decision problems in deep reinforcement learning.
method Proposes a simple remedy through addition of a randomized untrainable `prior' network to each ensemble member.
result The approach is efficient with linear representations and scales better than previous attempts to large-scale problems.
DP-RandP improves privacy-utility tradeoff in DP-SGD by learning priors from random processes.
problem Improving the performance of differentially private stochastic gradient descent (DP-SGD) on private data.
method A three-phase approach that learns priors from images generated by random processes and transfers these priors to private data.
result New state-of-the-art accuracy on CIFAR10, CIFAR100, MedMNIST, and ImageNet for various privacy budgets.
The paper optimizes trading strategies for assets modeled by a randomized Brownian bridge.
problem Optimizing trading strategies for assets with uninformative noise and unknown terminal prices.
method Modeling asset price evolution with an exponential randomized Brownian bridge and solving for optimal trading strategies numerically.
result Disconnected continuation/exercise regions appear under certain prior distributions.
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.
The paper shows how utility indifference prices approach superreplication prices in uncertain markets.
problem Modeling investor preferences under non-dominated uncertainty.
method Formulates and proves convergence of utility indifference prices to superreplication prices.
result Utility indifference prices converge to superreplication prices under certain conditions.
New PAC-Bayes method updates priors without losing confidence information.
problem Lack of sequential prior updates in PAC-Bayes without losing confidence information.
method Recursive PAC-Bayes decomposition of expected loss.
result Sequential prior updates with no information loss.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
New framework uses deep generative priors for robust phase retrieval.
problem Highly ill-posed and non-linear phase retrieval problem.
method Regularization through deep generative priors with gradient descent.
result Effective for random Gaussian and Fourier friendly measurements.
This paper analyzes and guarantees convergence of prior-guided ZO algorithms.
problem Understanding convergence properties of prior-guided zeroth-order optimization algorithms.
method Analysis of convergence under a greedy descent framework with various gradient estimators, and development of ARS algorithm.
result Convergence guarantee for prior-guided random gradient-free (PRGF) algorithms and accelerated random search (ARS) algorithm.
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.
A parametrization of hypergraphs based on the geometry of points in Rd is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or M…
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.
We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Mark…
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.
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
The paper introduces a new method for modeling correlations in high-dimensional data.
problem Modeling correlations among multiple dimensions in high-dimensional data.
method Population random measure embedding (PRME) using random functions and neural networks.
result The proposed method can efficiently learn correlations among multiple dimensions.
Master algorithm fails to detect non-stationarity in practical settings.
problem Non-Stationary Reinforcement Learning without prior knowledge.
method Master algorithm tested under various conditions, including piecewise stationary multi-armed bandits.
result Master's non-stationarity detection is ineffective for practical horizons, leading to performance similar to random restarting.
Improves black-box adversarial attacks with a transfer-based prior.
problem Low attack success rates and poor query efficiency in black-box adversarial attacks.
method P-RGF method that integrates a transfer-based prior and query information.
result Significantly reduces the number of queries needed for successful attacks.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Bayesian optimization improved for high-dimensional outputs using randomized priors.
problem Efficient global optimization of high-dimensional black-box functions.
method Deep learning framework with bootstrapped ensembles of neural architectures with randomized priors.
result Superior performance in tasks with high-dimensional outputs compared to state-of-the-art methods.
Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is made using a novel pseudo-marginal Metropolis-Hastings sampler for normalized comp…
Prior design is one of the most important problems in both statistics and machine learning. The cross validation (CV) and the widely applicable information criterion (WAIC) are predictive measures of the Bayesian estimation, however, it has been difficult to apply them to find the optimal prior because their mathematic…
Random neural networks produce functions with a number of knots equal to the number of neurons.
problem Understanding why neural networks with many parameters do not overfit early in training.
method Analyzing random scalar-input feed-forward rectified linear unit architectures, showing they are random linear splines.
result The number of knots in random neural networks is equal to the number of neurons, to very close approximation.
Two EM algorithms estimate prior distributions in mixture of linear regressions.
problem Estimating prior distributions in mixture of linear regressions.
method Two EM algorithms: one for continuous priors, one for discrete priors.
result Both algorithms accurately estimate prior distributions and the number of clusters.
Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.
problem Why randomly trained neural networks generalize well despite interpolating training data.
method Examined a random neural network that interpolates training data and showed it generalizes well if there's a simpler underlying teacher model.
result Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.
Bayesian tree ensemble model using horseshoe prior for regression and classification.
problem Flexible nonlinear regression and classification with many noisy predictors.
method Tree ensemble with rule-based predictors and horseshoe regularization.
result Outperforms state-of-the-art methods on 16 datasets.
Improved MRI head anatomy segmentation using deep learning with multiple priors.
problem Challenges in segmenting head anatomy in MRI, especially with lesions.
method Added three types of prior information to a 3D convolutional network: spatial priors, morphological priors, and spatial context.
result Multiprior network improves segmentation performance, especially for abnormal anatomies.
Develops methods for constructing parameter priors in DAG models.
problem Constructing parameter priors for model choice among DAG models.
method Introduces assumptions and methods for parameter priors construction and marginal likelihood computation.
result The only parameter prior for complete Gaussian DAG models that satisfies assumptions is the normal-Wishart distribution.
PCA can detect a low-rank signal in spiked random matrix models, but not always optimally.
problem Understanding when PCA can detect a low-rank signal in the presence of noise.
method Le Cam's notion of contiguity, analysis of spiked Wishart ensemble, and non-spectral tests.
result PCA is sub-optimal for detection in non-Gaussian Wigner ensembles and certain negative spikes in Gaussian Wishart ensemble.
Efficiently quantifies uncertainty in DeepONets for function spaces.
problem Uncertainty quantification in deep operator networks.
method Randomized prior ensembles for frequentist inference.
result Improved robustness and accuracy, reliable uncertainty estimates, out-of-distribution detection, and model bias quantification.
This paper proposes a framework for certifying neural network defenses against data poisoning attacks.
problem Vulnerability of neural networks to data poisoning attacks.
method Random selection based defenses that average predictions on sub-datasets sampled from the training set.
result The certified radius of bagging derived by the framework is tighter than previous work.
One-dimensional CNNs improve signal recovery from sparse measurements.
problem Recovering signals from limited data.
method One-dimensional Deep Image Prior (DIP) using CNNs with regularization.
result One-dimensional CNNs outperform traditional methods in signal recovery.
We consider the correlated multiarmed bandit (MAB) problem in which the rewards associated with each arm are modeled by a multivariate Gaussian random variable, and we investigate the influence of the assumptions in the Bayesian prior on the performance of the upper credible limit (UCL) algorithm and a new correlated U…
AI-driven Bayesian inference improves decision-making uncertainty.
problem Lack of certainty in AI predictions.
method Non-parametric Bayesian framework with Dirichlet process prior and AI-driven baseline.
result AI predictions can be integrated into Bayesian analysis for predictive inference and uncertainty quantification.
Study tests financial market efficiency using random number generator tests.
problem Check for informational efficiencies in financial markets.
method Analysed binary daily returns as random number generators, split analysis by annual and company levels, investigated longer-term efficiency over Nasdaq-listed companies.
result Information efficiency varies across years and reflects large-scale market impacts.
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.
Entropy-SGD optimizes a PAC-Bayes bound, leading to improved generalization.
problem Improving generalization in machine learning models.
method Entropy-SGD optimizes a PAC-Bayes bound by adjusting the prior, which is typically chosen independently of the data.
result Entropy-SGD can yield relatively tight generalization bounds and still fit real labels.
Study explores geometric structure and prior for beta-logistic distribution.
problem Understanding the geometric structure and prior distributions of the beta-logistic distribution.
method Exploring dual geometric structure and uncovering α-parallel prior. result The beta-logistic distribution admits an α-parallel prior for any real number α. Efficient Thompson sampling for non-conjugate priors.
problem Thompson sampling's computational intractability with non-conjugate priors.
method Reformulate Thompson sampling as an optimization problem and use Gumbel-Max trick.
result Proposes an efficient algorithm for non-conjugate priors.
Finite-width neural networks use non-Gaussian priors, extending Gaussian process theory.
problem Understanding the behavior of neural networks with finite width.
method Perturbative extension of Gaussian process theory to finite-width neural networks, tracking preactivation distributions.
result Non-Gaussian processes as priors in finite-width neural networks.
Randomly initialized sentence encoders perform well on tasks, suggesting learning is key.
problem The role of sentence encoder architectures in language tasks.
method Random initialization and fixed architecture approach to evaluate sentence encoders.
result Priors do not leverage additional information, learning is necessary.
G-Net constructs binary neural networks with high accuracy using randomized binary embeddings.
problem Creating high-accuracy binary neural networks with theoretical guarantees.
method Proposes a novel floating-point G-Net family with randomized binary embeddings and theoretical accuracy guarantees.
result Empirically, G-Net achieves almost 30% higher accuracy on CIFAR-10 compared to prior HDC models.
New study shows limits to classifying brain activity from randomized EEG trials.
problem Classifying human brain activity from image stimuli using EEG is challenging.
method Used randomized trials on a larger dataset (20x) to avoid stimulus-time confound.
result Classification accuracy is marginally above chance and statistically significant.
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.
New methods improve black-box adversarial attacks with fewer queries.
problem Efficiently craft adversarial examples without access to gradients.
method Prior-guided random gradient-free algorithms based on biased sampling and gradient averaging.
result Both methods require fewer queries and achieve higher success rates.