Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and highly flexible model. We focus on alternative mixtures of GP experts, which model the joint distribution of the inputs and targets explicitly. We highlight issues of this approach in multi-dimensional input spaces, namely, poor scalability and the need for an unnecessarily large number of experts, degrading the predictive performance and increasing uncertainty. We construct a novel model to address these issues through a nested partitioning scheme that automatically infers the number of components at both levels. Multiple response types are accommodated through a generalised GP framework, while multiple input types are included through a factorised exponential family structure. We show the effectiveness of our approach in estimating a parsimonious probabilistic description of both synthetic data of increasing dimension and an Alzheimer's challenge dataset.

Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions between items. These so-called symmetric DPPs have significant expressive power, and have been successfully applied to a variety of machine learning tasks, including recommendation systems, information retrieval, and automatic summarization, among many others. Efficient algorithms for learning symmetric DPPs and sampling from these models have been reasonably well studied. However, relatively little attention has been given to nonsymmetric DPPs, which relax the symmetric constraint on the kernel. Nonsymmetric DPPs allow for both repulsive and attractive item interactions, which can significantly improve modeling power, resulting in a model that may better fit for some applications. We present a method that enables a tractable algorithm, based on maximum likelihood estimation, for learning nonsymmetric DPPs from data composed of observed subsets. Our method imposes a particular decomposition of the nonsymmetric kernel that enables such tractable learning algorithms, which we analyze both theoretically and experimentally. We evaluate our model on synthetic and real-world datasets, demonstrating improved predictive performance compared to symmetric DPPs, which have previously shown strong performance on modeling tasks associated with these datasets.

We propose a new framework of imposing monotonicity constraints in a Bayesian non-parametric setting. Our approach is based on numerical solutions of stochastic differential equations [Hedge, 2019]. We derive a non-parametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. We demonstrate the efficacy of the proposed model by providing competitive results to other probabilistic models of monotonic functions on a number of benchmark functions. In addition, we consider the utility of a monotonic constraint in hierarchical probabilistic models, such as deep Gaussian processes. These typically suffer difficulties in modelling and propagating uncertainties throughout the hierarchy that can lead to hidden layers collapsing to point estimates. We address this by constraining hidden layers to be monotonic and present novel procedures for learning and inference that maintain uncertainty. We illustrate the capacity and versatility of the proposed framework on the task of temporal alignment of time-series data where it is beneficial to preserve the uncertainty in the temporal warpings.

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approach: first, we transform this task into a constrained matrix completion problem with entries bounded in the unit interval [0, 1]; second, we propose two novel matrix factorization models that leverage our knowledge of the VFX environment. Our first approach, expertise matrix factorization (EMF), is an interpretable method that structures the latent factors as weighted user-item interplay. The second one, survival matrix factorization (SMF), is instead a probabilistic model for the underlying process defining employees' efficiencies. We show the effectiveness of our proposed models by extensive numerical tests on our VFX dataset and two additional datasets with values that are also bounded in the [0, 1] interval.

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of convergence of entropic OT for empirical measures. Our analysis improves exponentially on the bound of Genevay et al. (2019) and extends their work to unbounded measures. Second, we establish a central limit theorem for entropic OT, based on techniques developed by Del Barrio and Loubes (2019). Previously, such a result was only known for finite metric spaces. As an application of our results, we develop and analyze a new technique for estimating the entropy of a random variable corrupted by gaussian noise.

Predicting not only the target but also an accurate measure of uncertainty is important for many applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing approach for evaluating the calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new evaluation method that escapes this caveat using a simple histogram-based approach inspired by reliability diagrams used in classification tasks. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple scaling-based calibration that preforms well in our experimental tests. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

The 2016 United States presidential election has been characterized as a period of extreme divisiveness that was exacerbated on social media by the influence of fake news, trolls, and social bots. However, the extent to which the public became more polarized in response to these influences over the course of the election is not well understood. In this paper we propose IdeoTrace, a framework for (i) jointly estimating the ideology of social media users and news websites and (ii) tracing changes in user ideology over time. We apply this framework to the last two months of the election period for a group of 47508 Twitter users and demonstrate that both liberal and conservative users became more polarized over time.

In this paper, we develop a neural summarization model which can effectively process multiple input documents and distill Transformer architecture with the ability to encode documents in a hierarchical manner. We represent cross-document relationships via an attention mechanism which allows to share information as opposed to simply concatenating text spans and processing them as a flat sequence. Our model learns latent dependencies among textual units, but can also take advantage of explicit graph representations focusing on similarity or discourse relations. Empirical results on the WikiSum dataset demonstrate that the proposed architecture brings substantial improvements over several strong baselines.

High accuracy localisation technologies exist but are prohibitively expensive to deploy for large indoor spaces such as warehouses, factories, and supermarkets to track assets and people. However, these technologies can be used to lend their highly accurate localisation capabilities to low-cost, commodity, and less-accurate technologies. In this paper, we bridge this link by proposing a technology-agnostic calibration framework based on artificial intelligence to assist such low-cost technologies through highly accurate localisation systems. A single-layer neural network is used to calibrate less accurate technology using more accurate one such as BLE using UWB and UWB using a professional motion tracking system. On a real indoor testbed, we demonstrate an increase in accuracy of approximately 70% for BLE and 50% for UWB. Not only the proposed approach requires a very short measurement campaign, the low complexity of the single-layer neural network also makes it ideal for deployment on constrained devices typically for localisation purposes.

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). FLoP focuses on generalizing from short proofs to longer ones of similar structure. To achieve that, FLoP uses state-of-the-art RL approaches that were previously not applied in theorem proving. In particular, we show that curriculum learning significantly outperforms previous learning-based proof guidance on a synthetic dataset of increasingly difficult arithmetic problems.