In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The first part of the article reviews these two tools and shows how they are connected. In particular, we focus on the Gaussian process regression, which is the core of Bayesian machine learning, and the issue of hyperparameter selection. The second part is dedicated to two financial applications. We first consider the modeling of the term structure of interest rates. More precisely, we test the fitting method and compare the GP prediction and the random walk model. The second application is the construction of trend-following strategies, in particular the online estimation of trend and covariance windows.

This paper considers the design of optimal resource allocation policies in wireless communication systems which are generically modeled as a functional optimization problem with stochastic constraints. These optimization problems have the structure of a learning problem in which the statistical loss appears as a constraint, motivating the development of learning methodologies to attempt their solution. To handle stochastic constraints, training is undertaken in the dual domain. It is shown that this can be done with small loss of optimality when using near-universal learning parameterizations. In particular, since deep neural networks (DNN) are near-universal their use is advocated and explored. DNNs are trained here with a model-free primal-dual method that simultaneously learns a DNN parametrization of the resource allocation policy and optimizes the primal and dual variables. Numerical simulations demonstrate the strong performance of the proposed approach on a number of common wireless resource allocation problems.

Echo State Networks (ESNs) are recurrent neural networks that only train their output layer, thereby precluding the need to backpropagate gradients through time, which leads to significant computational gains. Nevertheless, a common issue in ESNs is determining its hyperparameters, which are crucial in instantiating a well performing reservoir, but are often set manually or using heuristics. In this work we optimize the ESN hyperparameters using Bayesian optimization which, given a limited budget of function evaluations, outperforms a grid search strategy. In the context of large volumes of time series data, such as light curves in the field of astronomy, we can further reduce the optimization cost of ESNs. In particular, we wish to avoid tuning hyperparameters per individual time series as this is costly; instead, we want to find ESNs with hyperparameters that perform well not just on individual time series but rather on groups of similar time series without sacrificing predictive performance significantly. This naturally leads to a notion of clusters, where each cluster is represented by an ESN tuned to model a group of time series of similar temporal behavior. We demonstrate this approach both on synthetic datasets and real world light curves from the MACHO survey. We show that our approach results in a significant reduction in the number of ESN models required to model a whole dataset, while retaining predictive performance for the series in each cluster.

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

Unlike common cancers, such as those of the prostate and breast, tumor grading in rare cancers is difficult and largely undefined because of small sample sizes, the sheer volume of time needed to undertake on such a task, and the inherent difficulty of extracting human-observed patterns. One of the most challenging examples is intrahepatic cholangiocarcinoma (ICC), a primary liver cancer arising from the biliary system, for which there is well-recognized tumor heterogeneity and no grading paradigm or prognostic biomarkers. In this paper, we propose a new unsupervised deep convolutional autoencoder-based clustering model that groups together cellular and structural morphologies of tumor in 246 ICC digitized whole slides, based on visual similarity. From this visual dictionary of histologic patterns, we use the clusters as covariates to train Cox-proportional hazard survival models. In univariate analysis, three clusters were significantly associated with recurrence-free survival. Combinations of these clusters were significant in multivariate analysis. In a multivariate analysis of all clusters, five showed significance to recurrence-free survival, however the overall model was not measured to be significant. Finally, a pathologist assigned clinical terminology to the significant clusters in the visual dictionary and found evidence supporting the hypothesis that collagen-enriched fibrosis plays a role in disease severity. These results offer insight into the future of cancer subtyping and show that computational pathology can contribute to disease prognostication, especially in rare cancers.

Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the research in this area is mainly focused on enhancing the sparse coding part of the problem. In contrast, we introduce a novel objective term in our proposed SSC framework which focuses on the separability of data points in the coding space. We also provide mathematical insights into how this local-separability term improves the clustering result of the SSC framework. Our proposed non-linear local SSC algorithm (NLSSC) also benefits from the efficient choice of its sparsity terms and constraints. The NLSSC algorithm is also formulated in the kernel-based framework (NLKSSC) which can represent the nonlinear structure of data. In addition, we address the possibility of having redundancies in sparse coding results and its negative effect on graph-based clustering problems. We introduce the link-restore post-processing step to improve the representation graph of non-negative SSC algorithms such as ours. Empirical evaluations on well-known clustering benchmarks show that our proposed NLSSC framework results in better clusterings compared to the state-of-the-art baselines and demonstrate the effectiveness of the link-restore post-processing in improving the clustering accuracy via correcting the broken links of the representation graph.

Multiple kernel learning (MKL) algorithms combine different base kernels to obtain a more efficient representation in the feature space. Focusing on discriminative tasks, MKL has been used successfully for feature selection and finding the significant modalities of the data. In such applications, each base kernel represents one dimension of the data or is derived from one specific descriptor. Therefore, MKL finds an optimal weighting scheme for the given kernels to increase the classification accuracy. Nevertheless, the majority of the works in this area focus on only binary classification problems or aim for linear separation of the classes in the kernel space, which are not realistic assumptions for many real-world problems. In this paper, we propose a novel multi-class MKL framework which improves the state-of-the-art by enhancing the local separation of the classes in the feature space. Besides, by using a sparsity term, our large-margin multiple kernel algorithm (LMMK) performs discriminative feature selection by aiming to employ a small subset of the base kernels. Based on our empirical evaluations on different real-world datasets, LMMK provides a competitive classification accuracy compared with the state-of-the-art algorithms in MKL. Additionally, it learns a sparse set of non-zero kernel weights which leads to a more interpretable feature selection and representation learning.

Reducing communication overhead is a big challenge for large-scale distributed training. To address this issue, we present a hierarchical averaging stochastic gradient descent (Hier-AVG) algorithm that reduces global reductions (averaging) by employing less costly local reductions. As a very general type of parallel SGD, Hier-AVG can reproduce several commonly adopted synchronous parallel SGD variants by adjusting its parameters. We establish standard convergence results of Hier-AVG for non-convex smooth optimization problems. Under the non-asymptotic scenario, we show that Hier-AVG with less frequent global averaging can sometimes have faster training speed. In addition, we show that more frequent local averaging with more participants involved can lead to faster training convergence. By comparing Hier-AVG with another distributed training algorithm K-AVG, we show that through deploying local averaging with less global averaging Hier-AVG can still achieve comparable training speed while constantly get better test accuracy. As a result, local averaging can serve as an alternative remedy to effectively reduce communication overhead when the number of learners is large. We test Hier-AVG with several state-of-the-art deep neural nets on CIFAR-10 to validate our analysis. Further experiments to compare Hier-AVG with K-AVG on ImageNet-1K also show Hier-AVG's superiority over K-AVG.

Learning from human feedback is a viable alternative to control design that does not require modelling or control expertise. Particularly, learning from corrective advice garners advantages over evaluative feedback as it is a more intuitive and scalable format. The current state-of-the-art in this field, COACH, has proven to be a effective approach for confined problems. However, it parameterizes the policy with Radial Basis Function networks, which require meticulous feature space engineering for higher order systems. We introduce Gaussian Process Coach (GPC), where feature space engineering is avoided by employing Gaussian Processes. In addition, we use the available policy uncertainty to 1) inquire feedback samples of maximal utility and 2) to adapt the learning rate to the teacher's learning phase. We demonstrate that the novel algorithm outperforms the current state-of-the-art in final performance, convergence rate and robustness to erroneous feedback in OpenAI Gym continuous control benchmarks, both for simulated and real human teachers.

Due to the high variance of policy gradients, on-policy optimization algorithms are plagued with low sample efficiency. In this work, we propose Augment-Reinforce-Merge (ARM) policy gradient estimator as an unbiased low-variance alternative to previous baseline estimators on tasks with binary action space, inspired by the recent ARM gradient estimator for discrete random variable models. We show that the ARM policy gradient estimator achieves variance reduction with theoretical guarantees, and leads to significantly more stable and faster convergence of policies parameterized by neural networks.