Following the growing success of generative neural networks in LHC simulations, the crucial question is how to control the networks and assign uncertainties to their event output. We show how Bayesian normalizing flows or invertible networks capture uncertainties from the training and turn them into an uncertainty on the event weight. Fundamentally, the interplay between density and uncertainty estimates indicates that these networks learn functions in analogy to parameter fits rather than binned event counts.

Background: Single-cell RNA sequencing (scRNA-seq) yields valuable insights about gene expression and gives critical information about complex tissue cellular composition. In the analysis of single-cell RNA sequencing, the annotations of cell subtypes are often done manually, which is time-consuming and irreproducible. Garnett is a cell-type annotation software based the on elastic net method. Besides cell-type annotation, supervised machine learning methods can also be applied to predict other cell phenotypes from genomic data. Despite the popularity of such applications, there is no existing study to systematically investigate the performance of those supervised algorithms in various sizes of scRNA-seq data sets. Methods and Results: This study evaluates 13 popular supervised machine learning algorithms to classify cell phenotypes, using published real and simulated data sets with diverse cell sizes. The benchmark contained two parts. In the first part, we used real data sets to assess the popular supervised algorithms' computing speed and cell phenotype classification performance. The classification performances were evaluated using AUC statistics, F1-score, precision, recall, and false-positive rate. In the second part, we evaluated gene selection performance using published simulated data sets with a known list of real genes. Conclusion: The study outcomes showed that ElasticNet with interactions performed best in small and medium data sets. NB was another appropriate method for medium data sets. In large data sets, XGB works excellent. Ensemble algorithms were not significantly superior to individual machine learning methods. Adding interactions to ElasticNet can help, and the improvement was significant in small data sets.

Supervised Causal Learning (SCL) aims to learn causal relations from observational data by accessing previously seen datasets associated with ground truth causal relations. This paper presents a first attempt at addressing a fundamental question: What are the benefits from supervision and how does it benefit? Starting from seeing that SCL is not better than random guessing if the learning target is non-identifiable a priori, we propose a two-phase paradigm for SCL by explicitly considering structure identifiability. Following this paradigm, we tackle the problem of SCL on discrete data and propose ML4C. The core of ML4C is a binary classifier with a novel learning target: it classifies whether an Unshielded Triple (UT) is a v-structure or not. Starting from an input dataset with the corresponding skeleton provided, ML4C orients each UT once it is classified as a v-structure. These v-structures are together used to construct the final output. To address the fundamental question of SCL, we propose a principled method for ML4C featurization: we exploit the vicinity of a given UT (i.e., the neighbors of UT in skeleton), and derive features by considering the conditional dependencies and structural entanglement within the vicinity. We further prove that ML4C is asymptotically perfect. Last but foremost, thorough experiments conducted on benchmark datasets demonstrate that ML4C remarkably outperforms other state-of-the-art algorithms in terms of accuracy, robustness, tolerance and transferability. In summary, ML4C shows promising results on validating the effectiveness of supervision for causal learning.

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) has become the most popular algorithm for aspect modeling. While sufficiently successful in text topic extraction from large corpora, VB is less successful in identifying aspects in the presence of limited data. We present a novel variational message passing algorithm as applied to Latent Dirichlet Allocation (LDA) and compare it with the gold standard VB and collapsed Gibbs sampling. In situations where marginalisation leads to non-conjugate messages, we use ideas from sampling to derive approximate update equations. In cases where conjugacy holds, Loopy Belief update (LBU) (also known as Lauritzen-Spiegelhalter) is used. Our algorithm, ALBU (approximate LBU), has strong similarities with Variational Message Passing (VMP) (which is the message passing variant of VB). To compare the performance of the algorithms in the presence of limited data, we use data sets consisting of tweets and news groups. Additionally, to perform more fine grained evaluations and comparisons, we use simulations that enable comparisons with the ground truth via Kullback-Leibler divergence (KLD). Using coherence measures for the text corpora and KLD with the simulations we show that ALBU learns latent distributions more accurately than does VB, especially for smaller data sets.

Models used for many important engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial difference between the numerical solutions of the model and the observations of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is substantial interest in reducing model errors, particularly through understanding their physics and sources and leveraging the rapid growth of observational data. Here we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation (DA) technique such as ensemble Kalman filter (EnKF) is first used to provide a noise-free analysis state of the system, which is then used in estimating the model error. Finally, an equation-discovery technique, such as the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, closed-form representation of the model error. Using the chaotic Kuramoto-Sivashinsky (KS) system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

We present the winning strategy of an electricity demand forecasting competition. This competition was organized to design new forecasting methods for unstable periods such as the one starting in Spring 2020. We rely on state-space models to adapt standard statistical and machine learning models. We claim that it achieves the right compromise between two extremes. On the one hand, purely time-series models such as autoregressives are adaptive in essence but fail to capture dependence to exogenous variables. On the other hand, machine learning methods allow to learn complex dependence to explanatory variables on a historical data set but fail to forecast non-stationary data accurately. The evaluation period of the competition was the occasion of trial and error and we put the focus on the final forecasting procedure. In particular, it was at the same time that a recent algorithm was designed to adapt the variances of a state-space model and we present the results of the final version only. We discuss day-today predictions nonetheless.

We introduce TyXe, a Bayesian neural network library built on top of Pytorch and Pyro. Our leading design principle is to cleanly separate architecture, prior, inference and likelihood specification, allowing for a flexible workflow where users can quickly iterate over combinations of these components. In contrast to existing packages TyXe does not implement any layer classes, and instead relies on architectures defined in generic Pytorch code. TyXe then provides modular choices for canonical priors, variational guides, inference techniques, and layer selections for a Bayesian treatment of the specified architecture. Sampling tricks for variance reduction, such as local reparameterization or flipout, are implemented as effect handlers, which can be applied independently of other specifications. We showcase the ease of use of TyXe to explore Bayesian versions of popular models from various libraries: toy regression with a pure Pytorch neural network; large-scale image classification with torchvision ResNets; graph neural networks based on DGL; and Neural Radiance Fields built on top of Pytorch3D. Finally, we provide convenient abstractions for variational continual learning. In all cases the change from a deterministic to a Bayesian neural network comes with minimal modifications to existing code, offering a broad range of researchers and practitioners alike practical access to uncertainty estimation techniques. The library is available at https://github.com/TyXe-BDL/TyXe.

An increasingly common use case for machine learning models is augmenting the abilities of human decision makers. For classification tasks where neither the human or model are perfectly accurate, a key step in obtaining high performance is combining their individual predictions in a manner that leverages their relative strengths. In this work, we develop a set of algorithms that combine the probabilistic output of a model with the class-level output of a human. We show theoretically that the accuracy of our combination model is driven not only by the individual human and model accuracies, but also by the model's confidence. Empirical results on image classification with CIFAR-10 and a subset of ImageNet demonstrate that such human-model combinations consistently have higher accuracies than the model or human alone, and that the parameters of the combination method can be estimated effectively with as few as ten labeled datapoints.

Width-based planning has shown promising results on Atari 2600 games using pixel input, while using substantially fewer environment interactions than reinforcement learning. Recent width-based approaches have computed feature vectors for each screen using a hand designed feature set or a variational autoencoder (VAE) trained on game screens, and prune screens that do not have novel features during the search. In this paper, we explore consideration of uncertainty in features generated by a VAE during width-based planning. Our primary contribution is the introduction of active learning to maximize the utility of screens observed during planning. Experimental results demonstrate that use of active learning strategies increases gameplay scores compared to alternative width-based approaches with equal numbers of environment interactions.

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust high-dimensional regression with coefficient thresholding, in which an efficient nonconvex estimation procedure is proposed through a thresholding function and the robust Huber loss. The proposed regularization method accounts for complex dependence structures in predictors and is robust against outliers in outcomes. Theoretically, we analyze rigorously the landscape of the population and empirical risk functions for the proposed method. The fine landscape enables us to establish both {statistical consistency and computational convergence} under the high-dimensional setting. The finite-sample properties of the proposed method are examined by extensive simulation studies. An illustration of real-world application concerns a scalar-on-image regression analysis for an association of psychiatric disorder measured by the general factor of psychopathology with features extracted from the task functional magnetic resonance imaging data in the Adolescent Brain Cognitive Development study.