Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding aging and inflammatory diseases. We propose a scalable hierarchical Bayesian spatial model, called BLESS, capable of handling binary responses by placing continuous spike-and-slab mixture priors on spatially-varying parameters and enforcing spatial dependency on the parameter dictating the amount of sparsity within the probability of inclusion. The use of mean-field variational inference with dynamic posterior exploration, which is an annealing-like strategy that improves optimization, allows our method to scale to large sample sizes. Our method also accounts for underestimation of posterior variance due to variational inference by providing an approximate posterior sampling approach based on Bayesian bootstrap ideas and spike-and-slab priors with random shrinkage targets. Besides accurate uncertainty quantification, this approach is capable of producing novel cluster size based imaging statistics, such as credible intervals of cluster size, and measures of reliability of cluster occurrence. Lastly, we validate our results via simulation studies and an application to the UK Biobank, a large-scale lesion mapping study with a sample size of 40,000 subjects.
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RNN-T is currently considered the industry standard in ASR due to its exceptional WERs in various benchmark tests and its ability to support seamless streaming and longform transcription. However, its biggest drawback lies in the significant discrepancy between its training and inference objectives. During training, RNN-T maximizes all alignment probabilities by teacher forcing, while during inference, it uses beam search which may not necessarily find the maximum probable alignment. Additionally, RNN-T's inability to experience mistakes during teacher forcing training makes it more problematic when a mistake occurs in inference. To address this issue, this paper proposes a Reinforcement Learning method that minimizes the gap between training and inference time. Our Edit Distance based RL (EDRL) approach computes rewards based on the edit distance, and trains the network at every action level. The proposed approach yielded SoTA WERs on LibriSpeech for the 600M Conformer RNN-T model.
We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in generative AI, reinforcement learning, and computational biology. We consider the common learning scenario where the data set consists of unlabeled data along with a smaller set of data with noisy reward labels. Our approach leverages a learned reward function on the smaller data set as a pseudolabeler. From a theoretical standpoint, we show that this directed generator can effectively learn and sample from the reward-conditioned data distribution. Additionally, our model is capable of recovering the latent subspace representation of data. Moreover, we establish that the model generates a new population that moves closer to a user-specified target reward value, where the optimality gap aligns with the off-policy bandit regret in the feature subspace. The improvement in rewards obtained is influenced by the interplay between the strength of the reward signal, the distribution shift, and the cost of off-support extrapolation. We provide empirical results to validate our theory and highlight the relationship between the strength of extrapolation and the quality of generated samples.
Analysis of high-dimensional data, where the number of covariates is larger than the sample size, is a topic of current interest. In such settings, an important goal is to estimate the signal level $\tau^2$ and noise level $\sigma^2$, i.e., to quantify how much variation in the response variable can be explained by the covariates, versus how much of the variation is left unexplained. This thesis considers the estimation of these quantities in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no responses $Y$. Our main research question is: how can one use the unlabeled data to better estimate $\tau^2$ and $\sigma^2$? We consider two frameworks: a linear regression model and a linear projection model in which linearity is not assumed. In the first framework, while linear regression is used, no sparsity assumptions on the coefficients are made. In the second framework, the linearity assumption is also relaxed and we aim to estimate the signal and noise levels defined by the linear projection. We first propose a naive estimator which is unbiased and consistent, under some assumptions, in both frameworks. We then show how the naive estimator can be improved by using zero-estimators, where a zero-estimator is a statistic arising from the unlabeled data, whose expected value is zero. In the first framework, we calculate the optimal zero-estimator improvement and discuss ways to approximate the optimal improvement. In the second framework, such optimality does no longer hold and we suggest two zero-estimators that improve the naive estimator although not necessarily optimally. Furthermore, we show that our approach reduces the variance for general initial estimators and we present an algorithm that potentially improves any initial estimator. Lastly, we consider four datasets and study the performance of our suggested methods.
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational parameters is twice the number of unknown model parameters. The resulting diagonal covariance structure coupled with unimodal behavior can be too restrictive when dealing with highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors in the form of Gaussian mixtures can capture any distribution to an arbitrary degree of accuracy while maintaining some analytical tractability. Variational inference with Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. Coupled with the existence of multiple local minima due to nonconvex trends in the loss functions often associated with variational inference, these challenges motivate the need for robust initialization procedures to improve the performance and scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with an optimization stage in model parameter space in which local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace method. Finally, the mixture weights are determined through constrained least squares regression. Robustness and scalability are demonstrated using synthetic tests. The methodology is applied to an inversion problem in structural dynamics involving unknown viscous damping coefficients.
We study the regret of reinforcement learning from offline data generated by a fixed behavior policy in an infinite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted $Q$-iteration (FQI), suggest a $O(1/\sqrt{n})$ convergence for regret, empirical behavior exhibits \emph{much} faster convergence. In this paper, we present a finer regret analysis that exactly characterizes this phenomenon by providing fast rates for the regret convergence. First, we show that given any estimate for the optimal quality function $Q^*$, the regret of the policy it defines converges at a rate given by the exponentiation of the $Q^*$-estimate's pointwise convergence rate, thus speeding it up. The level of exponentiation depends on the level of noise in the \emph{decision-making} problem, rather than the estimation problem. We establish such noise levels for linear and tabular MDPs as examples. Second, we provide new analyses of FQI and Bellman residual minimization to establish the correct pointwise convergence guarantees. As specific cases, our results imply $O(1/n)$ regret rates in linear cases and $\exp(-\Omega(n))$ regret rates in tabular cases. We extend our findings to general function approximation by extending our results to regret guarantees based on $L_p$-convergence rates for estimating $Q^*$ rather than pointwise rates, where $L_2$ guarantees for nonparametric $Q^*$-estimation can be ensured under mild conditions.
Change point detection is a commonly used technique in time series analysis, capturing the dynamic nature in which many real-world processes function. With the ever increasing troves of multivariate high-dimensional time series data, especially in neuroimaging and finance, there is a clear need for scalable and data-driven change point detection methods. Currently, change point detection methods for multivariate high-dimensional data are scarce, with even less available in high-level, easily accessible software packages. To this end, we introduce the R package fabisearch, available on the Comprehensive R Archive Network (CRAN), which implements the factorized binary search (FaBiSearch) methodology. FaBiSearch is a novel statistical method for detecting change points in the network structure of multivariate high-dimensional time series which employs non-negative matrix factorization (NMF), an unsupervised dimension reduction and clustering technique. Given the high computational cost of NMF, we implement the method in C++ code and use parallelization to reduce computation time. Further, we also utilize a new binary search algorithm to efficiently identify multiple change points and provide a new method for network estimation for data between change points. We show the functionality of the package and the practicality of the method by applying it to a neuroimaging and a finance data set. Lastly, we provide an interactive, 3-dimensional, brain-specific network visualization capability in a flexible, stand-alone function. This function can be conveniently used with any node coordinate atlas, and nodes can be color coded according to community membership (if applicable). The output is an elegantly displayed network laid over a cortical surface, which can be rotated in the 3-dimensional space.
This paper investigates the multiple testing problem for high-dimensional sparse binary sequences motivated by the crowdsourcing problem in machine learning. We adopt an empirical Bayes approach to estimate possibly sparse sequences with Bernoulli noises. We found a surprising result that the hard thresholding rule deduced from the spike-and-slab posterior is not optimal, even using a uniform prior. Two approaches are then proposed to calibrate the posterior for achieving the optimal signal detection boundary, and two multiple testing procedures are constructed based on these calibrated posteriors. Sharp frequentist theoretical results for these procedures are obtained, showing both can effectively control the false discovery rate uniformly for signals under a sparsity assumption. Numerical experiments are conducted to validate our theory in finite samples.
The number of modes in a probability density function is representative of the model's complexity and can also be viewed as the number of existing subpopulations. Despite its relevance, little research has been devoted to its estimation. Focusing on the univariate setting, we propose a novel approach targeting prediction accuracy inspired by some overlooked aspects of the problem. We argue for the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view blending global and local density properties. Our method builds upon a combination of flexible kernel estimators and parsimonious compositional splines. Feature exploration, model selection and mode testing are implemented in the Bayesian inference paradigm, providing soft solutions and allowing to incorporate expert judgement in the process. The usefulness of our proposal is illustrated through a case study in sports analytics, showcasing multiple companion visualisation tools. A thorough simulation study demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, our method emerges as a top-tier alternative offering innovative solutions for analysts.
COVID-19 has led to excess deaths around the world, however it remains unclear how the mortality of other causes of death has changed during the pandemic. Aiming at understanding the wider impact of COVID-19 on other death causes, we study Italian data set that consists of monthly mortality counts of different causes from January 2015 to December 2020. Due to the high dimensional nature of the data, we develop a model which combines conventional Poisson regression with tensor train decomposition to explore the lower dimensional residual structure of the data. We take a Bayesian approach, impose priors on model parameters. Posterior inference is performed using an efficient Metropolis-Hastings within Gibbs algorithm. The validity of our approach is tested in simulation studies. Our method not only identifies differential effects of interventions on cause specific mortality rates through the Poisson regression component, but also offers informative interpretations of the relationship between COVID-19 and other causes of death as well as latent classes that underline demographic characteristics, temporal patterns and causes of death respectively.
We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically and computationally) is investigated and two algorithms based on Gibbs sampling and Stochastic Localization are analyzed, both under the same (quite natural) statistical assumptions that also enable valid inference on the sparse planted signal. The benefit of the Stochastic Localization sampler is particularly prominent for data matrix that is not well-designed.
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