The Variational Auto-Encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidean counterpart, and can qualitatively and quantitatively better recover hierarchical structures. Papers published at the Neural Information Processing Systems Conference.

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand.

We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of this map is the functional space associated to the network, and it is an irreducible algebraic variety upon taking closure. This paper proposes the dimension of this variety as a precise measure of the expressive power of polynomial neural networks. We obtain several theoretical results regarding this dimension as a function of architecture, including an exact formula for high activation degrees, as well as upper and lower bounds on layer widths in order for deep polynomials networks to fill the ambient functional space.

Tensor-network techniques have recently proven useful in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions. These factorizations include non-negative tensor-trains/MPS, which are in correspondence with hidden Markov models, and Born machines, which are naturally related to the probabilistic interpretation of quantum circuits. When used to model probability distributions, they exhibit tractable likelihoods and admit efficient learning algorithms. Interestingly, we prove that there exist probability distributions for which there are unbounded separations between the resource requirements of some of these tensor-network factorizations.

This paper presents a software implementation of a general framework for time series interpretation based on abductive reasoning. The software provides a data model and a set of algorithms to make inference to the best explanation of a time series, resulting in a description in multiple abstraction levels of the processes underlying the time series. As a proof of concept, a comprehensive knowledge base for the electrocardiogram (ECG) domain is provided, so it can be used directly as a tool for ECG analysis. This tool has been successfully validated in several noteworthy problems, such as heartbeat classification or atrial fibrillation detection.

Interest in the field of Explainable Artificial Intelligence has been growing for decades, and has accelerated recently. As Artificial Intelligence models have become more complex, and often more opaque, with the incorporation of complex machine learning techniques, explainability has become more critical. Recently, researchers have been investigating and tackling explainability with a user-centric focus, looking for explanations to consider trustworthiness, comprehensibility, explicit provenance, and context-awareness. In this chapter, we leverage our survey of explanation literature in Artificial Intelligence and closely related fields and use these past efforts to generate a set of explanation types that we feel reflect the expanded needs of explanation for today's artificial intelligence applications. We define each type and provide an example question that would motivate the need for this style of explanation. We believe this set of explanation types will help future system designers in their generation and prioritization of requirements and further help generate explanations that are better aligned to users' and situational needs.

Explainability has been an important goal since the early days of Artificial Intelligence. Several approaches for producing explanations have been developed. However, many of these approaches were tightly coupled with the capabilities of the artificial intelligence systems at the time. With the proliferation of AI-enabled systems in sometimes critical settings, there is a need for them to be explainable to end-users and decision-makers. We present a historical overview of explainable artificial intelligence systems, with a focus on knowledge-enabled systems, spanning the expert systems, cognitive assistants, semantic applications, and machine learning domains. Additionally, borrowing from the strengths of past approaches and identifying gaps needed to make explanations user- and context-focused, we propose new definitions for explanations and explainable knowledge-enabled systems.

AutoML-Zero aims to automatically discover computer programs that can solve machine learning tasks, starting from empty or random programs and using only basic math operations. The goal is to simultaneously search for all aspects of an ML algorithm--including the model structure and the learning strategy--while employing minimal human bias. Despite AutoML-Zero's challenging search space, evolutionary search shows promising results by discovering linear regression with gradient descent, 2-layer neural networks with backpropagation, and even algorithms that surpass hand designed baselines of comparable complexity. The figure above shows an example sequence of discoveries from one of our experiments, evolving algorithms to solve binary classification tasks. Notably, the evolved algorithms can be interpreted.

Life's most valuable asset is health. Continuously understanding the state of our health and modeling how it evolves is essential if we wish to improve it. Given the opportunity that people live with more data about their life today than any other time in history, the challenge rests in interweaving this data with the growing body of knowledge to compute and model the health state of an individual continually. This dissertation presents an approach to build a personal model and dynamically estimate the health state of an individual by fusing multi-modal data and domain knowledge. The system is stitched together from four essential abstraction elements: 1. the events in our life, 2. the layers of our biological systems (from molecular to an organism), 3. the functional utilities that arise from biological underpinnings, and 4. how we interact with these utilities in the reality of daily life. Connecting these four elements via graph network blocks forms the backbone by which we instantiate a digital twin of an individual. Edges and nodes in this graph structure are then regularly updated with learning techniques as data is continuously digested. Experiments demonstrate the use of dense and heterogeneous real-world data from a variety of personal and environmental sensors to monitor individual cardiovascular health state. State estimation and individual modeling is the fundamental basis to depart from disease-oriented approaches to a total health continuum paradigm. Precision in predicting health requires understanding state trajectory. By encasing this estimation within a navigational approach, a systematic guidance framework can plan actions to transition a current state towards a desired one. This work concludes by presenting this framework of combining the health state and personal graph model to perpetually plan and assist us in living life towards our goals.

Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on learning theory for general loss functions and hypothesis spaces remain limited. To fill the gap, we study the risk performance of distributed empirical risk minimization (ERM) for general loss functions and hypothesis spaces. The main contributions are two-fold. First, we derive two tight risk bounds under certain basic assumptions on the hypothesis space, as well as the smoothness, Lipschitz continuity, strong convexity of the loss function. Second, we further develop a more general risk bound for distributed ERM without the restriction of strong convexity.