Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of studies, observations, or measured variables increase. To address this issue, we propose variational inference algorithms to approximate the posterior distribution of Bayesian latent factor models using the multiplicative gamma process shrinkage prior. The proposed algorithms provide fast approximate inference at a fraction of the time and memory of MCMC-based implementations while maintaining comparable accuracy in characterizing the data covariance matrix. We conduct extensive simulations to evaluate our proposed algorithms and show their utility in estimating the model for high-dimensional multi-study gene expression data in ovarian cancers. Overall, our proposed approaches enable more efficient and scalable inference for factor models, facilitating their use in high-dimensional settings.
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We propose a novel Bayesian-Optimistic Frequentist Upper Confidence Bound (BOF-UCB) algorithm for stochastic contextual linear bandits in non-stationary environments. This unique combination of Bayesian and frequentist principles enhances adaptability and performance in dynamic settings. The BOF-UCB algorithm utilizes sequential Bayesian updates to infer the posterior distribution of the unknown regression parameter, and subsequently employs a frequentist approach to compute the Upper Confidence Bound (UCB) by maximizing the expected reward over the posterior distribution. We provide theoretical guarantees of BOF-UCB's performance and demonstrate its effectiveness in balancing exploration and exploitation on synthetic datasets and classical control tasks in a reinforcement learning setting. Our results show that BOF-UCB outperforms existing methods, making it a promising solution for sequential decision-making in non-stationary environments.
Batch active learning is a popular approach for efficiently training machine learning models on large, initially unlabelled datasets by repeatedly acquiring labels for batches of data points. However, many recent batch active learning methods are white-box approaches and are often limited to differentiable parametric models: they score unlabeled points using acquisition functions based on model embeddings or first- and second-order derivatives. In this paper, we propose black-box batch active learning for regression tasks as an extension of white-box approaches. Crucially, our method only relies on model predictions. This approach is compatible with a wide range of machine learning models, including regular and Bayesian deep learning models and non-differentiable models such as random forests. It is rooted in Bayesian principles and utilizes recent kernel-based approaches. This allows us to extend a wide range of existing state-of-the-art white-box batch active learning methods (BADGE, BAIT, LCMD) to black-box models. We demonstrate the effectiveness of our approach through extensive experimental evaluations on regression datasets, achieving surprisingly strong performance compared to white-box approaches for deep learning models.
We present RETA (Relative Timing Analysis), a differential timing analysis technique to verify the impact of an update on the execution time of embedded software. Timing analysis is computationally expensive and labor intensive. Software updates render repeating the analysis from scratch a waste of resources and time, because their impact is inherently confined. To determine this boundary, in RETA we apply a slicing procedure that identifies all relevant code segments and a statement categorization that determines how to analyze each such line of code. We adapt a subset of RETA for integration into aiT, an industrial timing analysis tool, and also develop a complete implementation in a tool called DELTA. Based on staple benchmarks and realistic code updates from official repositories, we test the accuracy by analyzing the worst-case execution time (WCET) before and after an update, comparing the measures with the use of the unmodified aiT as well as real executions on embedded hardware. DELTA returns WCET information that ranges from exactly the WCET of real hardware to 148% of the new version's measured WCET. With the same benchmarks, the unmodified aiT estimates are 112% and 149% of the actual executions; therefore, even when DELTA is pessimistic, an industry-strength tool such as aiT cannot do better. Crucially, we also show that RETA decreases aiT's analysis time by 45% and its memory consumption by 8.9%, whereas removing RETA from DELTA, effectively rendering it a regular timing analysis tool, increases its analysis time by 27%.
Comparing the survival times among two groups is a common problem in time-to-event analysis, for example if one would like to understand whether one medical treatment is superior to another. In the standard survival analysis setting, there has been a lot of discussion on how to quantify such difference and what can be an intuitive, easily interpretable, summary measure. In the presence of subjects that are immune to the event of interest (`cured'), we illustrate that it is not appropriate to just compare the overall survival functions. Instead, it is more informative to compare the cure fractions and the survival of the uncured sub-populations separately from each other. Our research is mainly driven by the question: if the cure fraction is similar for two available treatments, how else can we determine which is preferable? To this end, we estimate the mean survival times in the uncured fractions of both treatment groups ($MST_u$) and develop permutation tests for inference. In the first out of two connected papers, we focus on nonparametric approaches. The methods are illustrated with medical data of leukemia patients. In Part II we adjust the mean survival time of the uncured for potential confounders, which is crucial in observational settings. For each group, we employ the widely used logistic-Cox mixture cure model and estimate the $MST_u$ conditionally on a given covariate value. An asymptotic and a permutation-based approach have been developed for making inference on the difference of conditional $MST_u$'s between two groups. Contrarily to available results in the literature, in the simulation study we do not observe a clear advantage of the permutation method over the asymptotic one to justify its increased computational cost. The methods are illustrated through a practical application to breast cancer data.
The aim of this paper is to describe a novel non-parametric noise reduction technique from the point of view of Bayesian inference that may automatically improve the signal-to-noise ratio of one- and two-dimensional data, such as e.g. astronomical images and spectra. The algorithm iteratively evaluates possible smoothed versions of the data, the smooth models, obtaining an estimation of the underlying signal that is statistically compatible with the noisy measurements. Iterations stop based on the evidence and the $\chi^2$ statistic of the last smooth model, and we compute the expected value of the signal as a weighted average of the whole set of smooth models. In this paper, we explain the mathematical formalism and numerical implementation of the algorithm, and we evaluate its performance in terms of the peak signal to noise ratio, the structural similarity index, and the time payload, using a battery of real astronomical observations. Our Fully Adaptive Bayesian Algorithm for Data Analysis (FABADA) yields results that, without any parameter tuning, are comparable to standard image processing algorithms whose parameters have been optimized based on the true signal to be recovered, something that is impossible in a real application. State-of-the-art non-parametric methods, such as BM3D, offer slightly better performance at high signal-to-noise ratio, while our algorithm is significantly more accurate for extremely noisy data (higher than $20-40\%$ relative errors, a situation of particular interest in the field of astronomy). In this range, the standard deviation of the residuals obtained by our reconstruction may become more than an order of magnitude lower than that of the original measurements. The source code needed to reproduce all the results presented in this report, including the implementation of the method, is publicly available at //github.com/PabloMSanAla/fabada
Multi-task learning has emerged as a powerful machine learning paradigm for integrating data from multiple sources, leveraging similarities between tasks to improve overall model performance. However, the application of multi-task learning to real-world settings is hindered by data-sharing constraints, especially in healthcare settings. To address this challenge, we propose a flexible multi-task learning framework utilizing summary statistics from various sources. Additionally, we present an adaptive parameter selection approach based on a variant of Lepski's method, allowing for data-driven tuning parameter selection when only summary statistics are available. Our systematic non-asymptotic analysis characterizes the performance of the proposed methods under various regimes of the sample complexity and overlap. We demonstrate our theoretical findings and the performance of the method through extensive simulations. This work offers a more flexible tool for training related models across various domains, with practical implications in genetic risk prediction and many other fields.
Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real data set to estimate the extremal quantile treatment effect of college education on wage.
We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We show that previously developed estimators and confidence intervals (CIs) might be heavily biased and size-distorted when some of the factors are weak. We propose estimators with improved rates of convergence and bias-aware CIs that are uniformly valid regardless of whether the factors are strong or not. Our approach applies the theory of minimax linear estimation to form a debiased estimate using a nuclear norm bound on the error of an initial estimate of the interactive fixed effects. We use the obtained estimate to construct a bias-aware CI taking into account the remaining bias due to weak factors. In Monte Carlo experiments, we find a substantial improvement over conventional approaches when factors are weak, with little cost to estimation error when factors are strong.
As sequential neural architectures become deeper and more complex, uncertainty estimation is more and more challenging. Efforts in quantifying uncertainty often rely on specific training procedures, and bear additional computational costs due to the dimensionality of such models. In this paper, we propose to decompose a classification or regression task in two steps: a representation learning stage to learn low-dimensional states, and a state space model for uncertainty estimation. This approach allows to separate representation learning and design of generative models. We demonstrate how predictive distributions can be estimated on top of an existing and trained neural network, by adding a state space-based last layer whose parameters are estimated with Sequential Monte Carlo methods. We apply our proposed methodology to the hourly estimation of Electricity Transformer Oil temperature, a publicly benchmarked dataset. Our model accounts for the noisy data structure, due to unknown or unavailable variables, and is able to provide confidence intervals on predictions.
Supervised learning problems with side information in the form of a network arise frequently in applications in genomics, proteomics and neuroscience. For example, in genetic applications, the network side information can accurately capture background biological information on the intricate relations among the relevant genes. In this paper, we initiate a study of Bayes optimal learning in high-dimensional linear regression with network side information. To this end, we first introduce a simple generative model (called the Reg-Graph model) which posits a joint distribution for the supervised data and the observed network through a common set of latent parameters. Next, we introduce an iterative algorithm based on Approximate Message Passing (AMP) which is provably Bayes optimal under very general conditions. In addition, we characterize the limiting mutual information between the latent signal and the data observed, and thus precisely quantify the statistical impact of the network side information. Finally, supporting numerical experiments suggest that the introduced algorithm has excellent performance in finite samples.
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