Stochastic kernel based dimensionality reduction methods have become popular in the last decade. The central component of these methods is a symmetric kernel that quantifies the vicinity of pairs of data points and a kernel-induced Markov chain. Typically, the Markov chain is fully specified by the kernel through row normalization. However, it may be desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Notably, no systematic framework exists to prescribe user-defined constraints on Markov chains. Here, we use a path entropy maximization based approach to derive Markov chains on data using a kernel and additional user-defined constraints. We illustrate the usefulness of the path entropy normalization procedure with multiple real and artificial data sets. All scripts are available at: https://github.com/dixitpd/maxcaldiffmap

Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a Bayesian neural network, which effectively turns off nodes that do not help explain the data. In this work, we propose several modeling and inference advances that consistently improve the compactness of the model learned while maintaining predictive performance, especially in smaller-sample settings including reinforcement learning.

Harshil Shah University College London Bowen Zheng University College London David Barber University College London & Alan Turing Institute Abstract We introduce the A ttentive Unsupervised T ext (W) riter (AUTR), which is a word level generative model for natural language. It uses a recurrent neural network with a dynamic attention and canvas memory mechanism to iteratively construct sentences. By viewing the state of the memory at intermediate stages and where the model is placing its attention, we gain insight into how it constructs sentences. We demonstrate that AUTR learns a meaningful latent representation for each sentence, and achieves competitive log-likelihood lower bounds whilst being computationally efficient. It is effective at generating and reconstructing sentences, as well as imputing missing words. 1 Introduction Latent variable models have recently enjoyed significant success when modelling images (Gregor et al. 2015; Rezende et al. 2016; Gulrajani et al. 2017), as well as sequential data such as handwriting and speech (Bayer and Osendorfer 2015; Chung et al. 2015). They specify a conditional distribution of observed data, given a set of hidden (latent) variables. The stochastic gradient varia-tional Bayes (SGVB) algorithm (Kingma and Welling 2014; Rezende, Mohamed, and Wierstra 2014) has made (approximate) maximum likelihood learning possible on a large scale in models where the true posterior distribution of the latent variables is not tractable.

Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requires lower memory, computation, and implementation effort than existing VI methods, while obtaining uncertainty estimates of comparable quality. Our empirical results confirm this and further suggest that the weight-perturbation in our algorithm could be useful for exploration in reinforcement learning and stochastic optimization.

Q-Ensembles are a model-free approach where input images are fed into different Q-networks and exploration is driven by the assumption that uncertainty is proportional to the variance of the output Q-values obtained. They have been shown to perform relatively well compared to other exploration strategies. Further, model-based approaches, such as encoder-decoder models have been used successfully for next frame prediction given previous frames. This paper proposes to integrate the model-free Q-ensembles and model-based approaches with the hope of compounding the benefits of both and achieving superior exploration as a result. Results show that a model-based trajectory memory approach when combined with Q-ensembles produces superior performance when compared to only using Q-ensembles.

This dissertation investigates the use of one-sided classification algorithms in the application of separating hazardous chlorinated solvents from other materials, based on their Raman spectra. The experimentation is carried out using a new one-sided classification toolkit that was designed and developed from the ground up. In the one-sided classification paradigm, the objective is to separate elements of the target class from all outliers. These one-sided classifiers are generally chosen, in practice, when there is a deficiency of some sort in the training examples. Sometimes outlier examples can be rare, expensive to label, or even entirely absent. However, this author would like to note that they can be equally applicable when outlier examples are plentiful but nonetheless not statistically representative of the complete outlier concept. It is this scenario that is explicitly dealt with in this research work. In these circumstances, one-sided classifiers have been found to be more robust that conventional multi-class classifiers. The term "unexpected" outliers is introduced to represent outlier examples, encountered in the test set, that have been taken from a different distribution to the training set examples. These are examples that are a result of an inadequate representation of all possible outliers in the training set. It can often be impossible to fully characterise outlier examples given the fact that they can represent the immeasurable quantity of "everything else" that is not a target. The findings from this research have shown the potential drawbacks of using conventional multi-class classification algorithms when the test data come from a completely different distribution to that of the training samples.

We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is consistent under certain conditions and that is quite robust to the violations of these conditions. In simulations, BGCF substantially outperforms two state-of-the-art alternative approaches. An illustration on the `Holzinger & Swineford 1939' dataset indicates that BGCF is favorable over the so-called robust maximum likelihood (MLR) even if the data match the assumptions of MLR.

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic model, even a simple modification of the underlying dynamical system requires significant physical intuition. This paper presents the first meta-learning algorithm that allows automated design for the underlying continuous dynamics of an SG-MCMC sampler. The learned sampler generalizes Hamiltonian dynamics with state-dependent drift and diffusion, enabling fast traversal and efficient exploration of neural network energy landscapes. Experiments validate the proposed approach on both Bayesian fully connected neural network and Bayesian recurrent neural network tasks, showing that the learned sampler out-performs generic, hand-designed SG-MCMC algorithms, and generalizes to different datasets and larger architectures.

We propose a method for maximizing a partial area under a receiver operating characteristic (ROC) curve (pAUC) for binary classification tasks. In binary classification tasks, accuracy is the most commonly used as a measure of classifier performance. In some applications such as anomaly detection and diagnostic testing, accuracy is not an appropriate measure since prior probabilties are often greatly biased. Although in such cases the pAUC has been utilized as a performance measure, few methods have been proposed for directly maximizing the pAUC. This optimization is achieved by using a scoring function. The conventional approach utilizes a linear function as the scoring function. In contrast we newly introduce nonlinear scoring functions for this purpose. Specifically, we present two types of nonlinear scoring functions based on generative models and deep neural networks. We show experimentally that nonlinear scoring fucntions improve the conventional methods through the application of a binary classification of real and bogus objects obtained with the Hyper Suprime-Cam on the Subaru telescope.

Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyses how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's actions on quoted prices and the prices they receive from trading. Under fairly general assumptions, we demonstrate how the trader can learn the posterior distribution over the latent states, and explicitly solve the latent optimal trading problem. We provide a verification theorem, and a methodology for calibrating the model by deriving a variation of the expectation-maximization algorithm. To illustrate the efficacy of the optimal strategy, we demonstrate its performance through simulations and compare it to strategies which ignore learning in the latent factors. We also provide calibration results for a particular model using Intel Corporation stock as an example.