Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including "sampled ancestors" in which we sequence a genotype along with its direct descendants, and "polytomies" in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches in the tree. However, current maximum-likelihood based approaches are not capable of revealing such zero-length branches. In this paper, we find these zero-length branches by introducing adaptive-LASSO-type regularization estimators to phylogenetics, deriving their properties, and showing regularization to be a practically useful approach for phylogenetics.

In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is hardly sustainable in large-scale problems and devising efficient alternatives is a challenge. In this work, we investigate if and how Gaussian process regression directly applied to the classification labels can be used to tackle this question. While in this case training time is remarkably faster, predictions need be calibrated for classification and uncertainty estimation. To this aim, we propose a novel approach based on interpreting the labels as the output of a Dirichlet distribution. Extensive experimental results show that the proposed approach provides essentially the same accuracy and uncertainty quantification of Gaussian process classification while requiring only a fraction of computational resources.

Collecting the large datasets needed to train deep neural networks can be very difficult, particularly for the many applications for which sharing and pooling data is complicated by practical, ethical, or legal concerns. However, it may be the case that derivative datasets or predictive models developed within individual sites can be shared and combined with fewer restrictions. Training on distributed datasets and combining the resulting networks is often viewed as continual learning, but these methods require networks to be trained sequentially. In this paper, we introduce parallel weight consolidation (PWC), a continual learning method to consolidate the weights of neural networks trained in parallel on independent datasets. We perform a brain segmentation case study using PWC to consolidate several dilated convolutional neural networks trained in parallel on independent structural magnetic resonance imaging (sMRI) datasets from different sites. We found that PWC led to increased performance on held-out test sets from the different sites, as well as on a very large and completely independent multi-site dataset. This demonstrates the feasibility of PWC for combining the knowledge learned by networks trained on different datasets.

Methods in Economics TU Vienna In this work we introduce a novel paradigm for Bayesian learning based on optimal transport theory. Namely, we propose to use the Wasserstein barycenter of the posterior law on models, as an alternative to the maximum a posteriori estimator (MAP) and Bayes predictive distributions. We exhibit conditions granting the existence and consistency of this estimator, discuss some of its basic and specific properties, and propose a numerical approximation relying on standard posterior sampling in general finite-dimensional parameter spaces. We thus also contribute to the recent blooming of applications of optimal transport theory in machine learning, beyond the discrete and semidiscrete settings so far considered. Advantages of the proposed estimator are discussed and illustrated with numerical simulations.

Frequentist-leaning statisticians have numerous responses to Bayesian criticisms that may not be widely known. Broadly speaking, these rebuttals assert that Bayesian criticisms of Frequentist approaches rely on circular arguments, are self-refuting, rest mostly on semantics, or are mainly of interest to academics and irrelevant in practice. Below, I've briefly summarized the ones I'm aware of from memory and in my own words. The meaning of the term is often unclear. Is it objective Bayes, subjective Bayes, approximate Bayes, empirical Bayes, or all of the above?

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempster's multivalued mappings and lower and upper probabilities and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set if those sets are related by a partial monotone S-approximation space.

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes (e.g., information diffusion, virus propagation) occurring over the unobserved network. While there have been efforts to infer networks based on such data, providing a generative probabilistic model that is able to identify the underlying time-varying network remains an open question. Here we consider the problem of inferring generative dynamic network models based on network cascade diffusion data. We propose a novel framework for providing a non-parametric dynamic network model--based on a mixture of coupled hierarchical Dirichlet processes-- based on data capturing cascade node infection times. Our approach allows us to infer the evolving community structure in networks and to obtain an explicit predictive distribution over the edges of the underlying network--including those that were not involved in transmission of any cascade, or are likely to appear in the future. We show the effectiveness of our approach using extensive experiments on synthetic as well as real-world networks.

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. All current methods are based on extracting uncertainty signals from a trained network optimized to solve the classification problem at hand. We demonstrate that such techniques tend to misestimate instances whose predictions are supposed to be highly confident. This deficiency is an artifact of the training process with SGD-like optimizers. Based on this observation, we develop an uncertainty estimation algorithm that "peels away" highly confident points sequentially and estimates their confidence using earlier snapshots of the trained model, before their uncertainty estimates are jittered. We present extensive experiments indicating that the proposed algorithm provides uncertainty estimates that are consistently better than the best known methods.

Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in the posterior regularization framework. SSDKL combines the hierarchical representation learning of neural networks with the probabilistic modeling capabilities of Gaussian processes. By leveraging unlabeled data, we show improvements on a diverse set of real-world regression tasks over supervised deep kernel learning and semi-supervised methods such as VAT and mean teacher adapted for regression.

Probabilistic modelling is a general and elegant framework to capture the uncertainty, ambiguity and diversity of hidden structures in data. Probabilistic inference is the key operation on probabilistic models to obtain the distribution over the latent representations given data. Unfortunately, the computation of inference on complex models is extremely challenging. In spite of the success of existing inference methods, like Markov chain Monte Carlo(MCMC) and variational inference(VI), many powerful models are not available for large scale problems because inference is simply computationally intractable. The recent advances in using neural networks for probabilistic inference have shown promising results on this challenge. In this work, we propose a novel general inference framework that has the strength from both MCMC and VI. The proposed method is not only computationally scalable and efficient, but also has its root from the ergodicity theorem, that provides the guarantee of better performance with more computational power. Our experiment results suggest that our method can outperform state-of-the-art methods on generative models and Bayesian neural networks on some popular benchmark problems.