Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum likelihood objective. Due to the inherent structure of such models, classical regularization approaches in the parameter space are rendered ineffective. To address this issue, we develop a model-agnostic noise regularization method for CDE that adds random perturbations to the data during training. We demonstrate that the proposed approach corresponds to a smoothness regularization and prove its asymptotic consistency. In our experiments, noise regularization significantly and consistently outperforms other regularization methods across seven data sets and three CDE models. The effectiveness of noise regularization makes neural network based CDE the preferable method over previous non- and semi-parametric approaches, even when training data is scarce.

In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence variational inference is often required. In this approach, an evidence lower bound on the log likelihood of data is maximized during training. Variational Autoencoders (VAE) are one important example where variational inference is utilized. In this tutorial, we derive the variational lower bound loss function of the standard variational autoencoder. We do so in the instance of a gaussian latent prior and gaussian approximate posterior, under which assumptions the Kullback-Leibler term in the variational lower bound has a closed form solution. We derive essentially everything we use along the way; everything from Bayes' theorem to the Kullback-Leibler divergence.

Twitter @tarantulae 4. Uncertainty in Deep Learning - Christian S. Perone (2019) Uncertainties Bayesian Inference Deep Learning Variational Inference Ensembles Q&A Section I Uncertainties 5. Uncertainty in Deep Learning - Christian S. Perone (2019) Uncertainties Bayesian Inference Deep Learning Variational Inference Ensembles Q&A Knowing what you don't know It is correct, somebody might say, that (...) Socrates did not know anything; and it was indeed wisdom that they recognized their own lack of knowledge, (...).

Predicting the remaining useful life of machinery, infrastructure, or other equipment can facilitate preemptive maintenance decisions, whereby a failure is prevented through timely repair or replacement. This allows for a better decision support by considering the anticipated time-to-failure and thus promises to reduce costs. Here a common baseline may be derived by fitting a probability density function to past lifetimes and then utilizing the (conditional) expected remaining useful life as a prognostic. This approach finds widespread use in practice because of its high explanatory power. A more accurate alternative is promised by machine learning, where forecasts incorporate deterioration processes and environmental variables through sensor data. However, machine learning largely functions as a black-box method and its forecasts thus forfeit most of the desired interpretability. As our primary contribution, we propose a structured-effect neural network for predicting the remaining useful life which combines the favorable properties of both approaches: its key innovation is that it offers both a high accountability and the flexibility of deep learning. The parameters are estimated via variational Bayesian inferences. The different approaches are compared based on the actual time-to-failure for aircraft engines. This demonstrates the performance and superior interpretability of our method, while we finally discuss implications for decision support.

End-to-end learning has recently emerged as a promising technique to tackle the problem of autonomous driving. Existing works show that learning a navigation policy from raw sensor data may reduce the system's reliance on external sensing systems, (e.g. GPS), and/or outperform traditional methods based on state estimation and planning. However, existing end-to-end methods generally trade off performance for safety, hindering their diffusion to real-life applications. For example, when confronted with an input which is radically different from the training data, end-to-end autonomous driving systems are likely to fail, compromising the safety of the vehicle. To detect such failure cases, this work proposes a general framework for uncertainty estimation which enables a policy trained end-to-end to predict not only action commands, but also a confidence about its own predictions. In contrast to previous works, our framework can be applied to any existing neural network and task, without the need to change the network's architecture or loss, or to train the network. In order to do so, we generate confidence levels by forward propagation of input and model uncertainties using Bayesian inference. We test our framework on the task of steering angle regression for an autonomous car, and compare our approach to existing methods with both qualitative and quantitative results on a real dataset. Finally, we show an interesting by-product of our framework: robustness against adversarial attacks.

The success of generative modeling in continuous domains has led to a surge of interest in generating discrete data such as molecules, source code, and graphs. However, construction histories for these discrete objects are typically not unique and so generative models must reason about intractably large spaces in order to learn. Additionally, structured discrete domains are often characterized by strict constraints on what constitutes a valid object and generative models must respect these requirements in order to produce useful novel samples. Here, we present a generative model for discrete objects employing a Markov chain where transitions are restricted to a set of local operations that preserve validity. Building off of generative interpretations of denoising autoencoders, the Markov chain alternates between producing 1) a sequence of corrupted objects that are valid but not from the data distribution, and 2) a learned reconstruction distribution that attempts to fix the corruptions while also preserving validity. This approach constrains the generative model to only produce valid objects, requires the learner to only discover local modifications to the objects, and avoids marginalization over an unknown and potentially large space of construction histories. We evaluate the proposed approach on two highly structured discrete domains, molecules and Laman graphs, and find that it compares favorably to alternative methods at capturing distributional statistics for a host of semantically relevant metrics.

Prevalent efforts have been put in automatically inferring genres of musical items. Yet, the propose solutions often rely on simplifications and fail to address the diversity and subjectivity of music genres. Accounting for these has, though, many benefits for aligning knowledge sources, integrating data and enriching musical items with tags. Here, we choose a new angle for the genre study by seeking to predict what would be the genres of musical items in a target tag system, knowing the genres assigned to them within source tag systems. We call this a translation task and identify three cases: 1) no common annotated corpus between source and target tag systems exists, 2) such a large corpus exists, 3) only few common annotations exist. We propose the related solutions: a knowledge-based translation modeled as taxonomy mapping, a statistical translation modeled with maximum likelihood logistic regression; a hybrid translation modeled with maximum a posteriori logistic regression with priors given by the knowledge-based translation. During evaluation, the solutions fit well the identified cases and the hybrid translation is systematically the most effective w.r.t. multilabel classification metrics. This is a first attempt to unify genre tag systems by leveraging both representation and interpretation diversity.

We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization when there is information available on the underlying true probability distribution. The methods we evaluate are (a) bagging; (b) kernel smoothing; (c) maximum likelihood estimation (MLE); and (d) a Bayesian approach. We use two test sets, the first has a quadratic objective function allowing for very different types of interaction between the random component and the univariate decision variable. Here the sample average approximation is remarkably effective and only consistently outperformed by a Bayesian approach. The second test set is a portfolio optimization problem in which we use different covariance structures for a set of 5 stocks. Here bagging, MLE and a Bayesian approach all do well.

Upcoming synoptic surveys are set to generate an unprecedented amount of data. This requires an automatic framework that can quickly and efficiently provide classification labels for several new object classification challenges. Using data describing 11 types of variable stars from the Catalina Real-Time Transient Surveys (CRTS), we illustrate how to capture the most important information from computed features and describe detailed methods of how to robustly use Information Theory for feature selection and evaluation. We apply three Machine Learning (ML) algorithms and demonstrate how to optimize these classifiers via cross-validation techniques. For the CRTS dataset, we find that the Random Forest (RF) classifier performs best in terms of balanced-accuracy and geometric means. We demonstrate substantially improved classification results by converting the multi-class problem into a binary classification task, achieving a balanced-accuracy rate of $\sim$99 per cent for the classification of ${\delta}$-Scuti and Anomalous Cepheids (ACEP). Additionally, we describe how classification performance can be improved via converting a 'flat-multi-class' problem into a hierarchical taxonomy. We develop a new hierarchical structure and propose a new set of classification features, enabling the accurate identification of subtypes of cepheids, RR Lyrae and eclipsing binary stars in CRTS data.

We propose sparse estimation methods for the generalized linear models, which run Least Angle Regression (LARS) and Least Absolute Shrinkage and Selection Operator (LASSO) in the tangent space of the manifold of the statistical model. Our approach is to roughly approximate the statistical model and to subsequently use exact calculations. LARS was proposed as an efficient algorithm for parameter estimation and variable selection for the normal linear model. The LARS algorithm is described in terms of Euclidean geometry with regarding correlation as metric of the space. Since the LARS algorithm only works in Euclidean space, we transform a manifold of the statistical model into the tangent space at the origin. In the generalized linear regression, this transformation allows us to run the original LARS algorithm for the generalized linear models. The proposed methods are efficient and perform well. Real-data analysis shows that the proposed methods output similar results as that of the $l_1$-penalized maximum likelihood estimation for the generalized linear models. Numerical experiments show that our methods work well and they can be better than the $l_1$-penalization for the generalized linear models in generalization, parameter estimation, and model selection.