Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical CNN architectures in computer vision only compound this problem. Uncertainty in neural networks has thus been largely ignored in practice, despite the fact that it may provide important information about the reliability of predictions and the inner workings of the network. In this paper, we introduce two lightweight approaches to making supervised learning with probabilistic deep networks practical: First, we suggest probabilistic output layers for classification and regression that require only minimal changes to existing networks. Second, we employ assumed density filtering and show that activation uncertainties can be propagated in a practical fashion through the entire network, again with minor changes. Both probabilistic networks retain the predictive power of the deterministic counterpart, but yield uncertainties that correlate well with the empirical error induced by their predictions. Moreover, the robustness to adversarial examples is significantly increased.

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gibbs sampling and an approximate variational mean field approach. For the latter we utilise sparse GP approximations to tackle the infinite dimensionality of the problem. The performance of both algorithms and comparisons with other density estimators are demonstrated on artificial and real datasets with up to several thousand data points.

Using movement primitive libraries is an effective means to enable robots to solve more complex tasks. In order to build these movement libraries, current algorithms require a prior segmentation of the demonstration trajectories. A promising approach is to model the trajectory as being generated by a set of Switching Linear Dynamical Systems and inferring a meaningful segmentation by inspecting the transition points characterized by the switching dynamics. With respect to the learning, a nonparametric Bayesian approach is employed utilizing a Gibbs sampler.

Motivated by the widespread adoption of large-scale A/B testing in industry, we propose a new experimentation framework for the setting where potential experiments are abundant (i.e., many hypotheses are available to test), and observations are costly; we refer to this as the experiment-rich regime. Such scenarios require the experimenter to internalize the opportunity cost of assigning a sample to a particular experiment. We fully characterize the optimal policy and give an algorithm to compute it. Furthermore, we develop a simple heuristic that also provides intuition for the optimal policy. We use simulations based on real data to compare both the optimal algorithm and the heuristic to other natural alternative experimental design frameworks. In particular, we discuss the paradox of power: high-powered classical tests can lead to highly inefficient sampling in the experiment-rich regime.

A framework is introduced for actively and adaptively solving a sequence of machine learning problems, which are changing in bounded manner from one time step to the next. An algorithm is developed that actively queries the labels of the most informative samples from an unlabeled data pool, and that adapts to the change by utilizing the information acquired in the previous steps. Our analysis shows that the proposed active learning algorithm based on stochastic gradient descent achieves a near-optimal excess risk performance for maximum likelihood estimation. Furthermore, an estimator of the change in the learning problems using the active learning samples is constructed, which provides an adaptive sample size selection rule that guarantees the excess risk is bounded for sufficiently large number of time steps. Experiments with synthetic and real data are presented to validate our algorithm and theoretical results.

In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful meta-classification network that can solve arbitrary classification problems without further training.

We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector and the true label, we bound the excess risk of an arbitrary classifier trained with imperfect labels in terms of its excess risk for predicting a noisy label. This reveals conditions under which a classifier trained with imperfect labels remains consistent for classifying uncorrupted test data points. Furthermore, under stronger conditions, we derive detailed asymptotic properties for the popular $k$-nearest neighbour ($k$nn), Support Vector Machine (SVM) and Linear Discriminant Analysis (LDA) classifiers. One consequence of these results is that the $k$nn and SVM classifiers are robust to imperfect training labels, in the sense that the rate of convergence of the excess risks of these classifiers remains unchanged; in fact, it even turns out that in some cases, imperfect labels may improve the performance of these methods. On the other hand, the LDA classifier is shown to be typically inconsistent in the presence of label noise unless the prior probabilities of each class are equal. Our theoretical results are supported by a simulation study.

This paper considers the problem of removing costly features from a Bayesian network classifier. We want the classifier to be robust to these changes, and maintain its classification behavior. To this end, we propose a closeness metric between Bayesian classifiers, called the expected classification agreement (ECA). Our corresponding trimming algorithm finds an optimal subset of features and a new classification threshold that maximize the expected agreement, subject to a budgetary constraint. It utilizes new theoretical insights to perform branch-and-bound search in the space of feature sets, while computing bounds on the ECA. Our experiments investigate both the runtime cost of trimming and its effect on the robustness and accuracy of the final classifier.

Technical analysis is used to discover investment opportunities. To test this hypothesis we propose an hybrid system using machine learning techniques together with genetic algorithms. Using technical analysis there are more ways to represent a currency exchange time series than the ones it is possible to test computationally, i.e., it is unfeasible to search the whole input feature space thus a genetic algorithm is an alternative. In this work, an architecture for automatic feature selection is proposed to optimize the cross validated performance estimation of a Naive Bayes model using a genetic algorithm. The proposed architecture improves the return on investment of the unoptimized system from 0,43% to 10,29% in the validation set. The features selected and the model decision boundary are visualized using the algorithm t-Distributed Stochastic Neighbor embedding.

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.