Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional distributions which cannot be meaningfully summarized using expectation only (due to e.g. multimodality). Hence, we consider the problem of conditional density estimation in the meta-learning setting. We introduce a novel technique for meta-learning which combines neural representation and noise-contrastive estimation with the established literature of conditional mean embeddings into reproducing kernel Hilbert spaces. The method is validated on synthetic and real-world problems, demonstrating the utility of sharing learned representations across multiple conditional density estimation tasks.

We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables using neural networks. This extension allows to model complex interactions while being more global in its search compared to other greedy approaches. In addition to comparing our method to existing continuous optimization methods, we provide missing empirical comparisons to nonlinear greedy search methods. On both synthetic and real-world data sets, this new method outperforms current continuous methods on most tasks while being competitive with existing greedy search methods on important metrics for causal inference.

Centuries of development in natural sciences and mathematical modeling provide valuable domain expert knowledge that has yet to be explored for the development of machine learning models. When modeling complex physical systems, both domain knowledge and data contribute important information about the system. In this paper, we present a data-driven model that takes advantage of partial domain knowledge in order to improve generalization and interpretability. The presented model, which we call EVGP (Explicit Variational Gaussian Process), uses an explicit linear prior to incorporate partial domain knowledge while using data to fill in the gaps in knowledge. Variational inference was used to obtain a sparse approximation that scales well to large datasets. The advantages include: 1) using partial domain knowledge to improve inductive bias (assumptions of the model), 2) scalability to large datasets, 3) improved interpretability. We show how the EVGP model can be used to learn system dynamics using basic Newtonian mechanics as prior knowledge. We demonstrate that using simple priors from partially defined physics models considerably improves performance when compared to fully data-driven models.

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based models are slow to invert, making either density estimation or sample generation slow. Flows based on coupling transforms are fast for both tasks, but have previously performed less well at density estimation than autoregressive flows. We stack a new coupling transform, based on monotonic cubic splines, with LU-decomposed linear layers. The resulting cubic-spline flow retains an exact one-pass inverse, can be used to generate high-quality images, and closes the gap with autoregressive flows on a suite of density-estimation tasks.

We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve this broader goal. We formally derive a biologically-inspired neural network from Nystr\"om kernel approximations and empirically demonstrate that the network successfully approximates transition distributions. The proposed network yields representations that, just like place cells, soft-tile the input space with highly sparse and localized receptive fields. Additionally, we show that the proposed computational motif can be extended to handle supervised problems, creating class-specific place cells while exhibiting low sample complexity.

In recent years, deep reinforcement learning has pushed the boundaries of Artificial Intelligence to an unprecedented level, achieving what was expected to be possible only in a decade and outperforming human intelligence in a number of highly complex tasks. Paramount examples of this potential have appeared over the past few years, with such algorithms mastering games and tasks of increasing complexity, from playing Atari to learning to walk and beating world grandmasters at the game of Go [16, 23, 24, 31-33]. Such impressive success would be impossible without using neural networks to approximate value functions and / or policy functions in reinforcement learning algorithms. While neural networks, in particular deep neural networks, provide a powerful and versatile tool to approximate high dimensional functions [4, 12, 17], their intrinsic nonlinearity might also lead to trouble in training, in particular in the context of reinforcement learning. For example, it is well known that nonlinear approximation to value function might cause divergence in the classical temporal-difference learning due to instability [40].

We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued function. While these problems can be solved with standard Bayesian optimization, we propose a novel approach that exploits the composite structure of the objective function to substantially improve sampling efficiency. Our approach models $h$ using a multi-output Gaussian process and chooses where to sample using the expected improvement evaluated on the implied non-Gaussian posterior on $f$, which we call expected improvement for composite functions (\ei). Although \ei\ cannot be computed in closed form, we provide a novel stochastic gradient estimator that allows its efficient maximization. We also show that our approach is asymptotically consistent, i.e., that it recovers a globally optimal solution as sampling effort grows to infinity, generalizing previous convergence results for classical expected improvement. Numerical experiments show that our approach dramatically outperforms standard Bayesian optimization benchmarks, reducing simple regret by several orders of magnitude.

Chart-based visual acuity measurements are used by billions of people to diagnose and guide treatment of vision impairment. However, the ubiquitous eye exam has no mechanism for reasoning about uncertainty and as such, suffers from a well-documented reproducibility problem. In this paper we uncover a new parametric probabilistic model of visual acuity response based on measurements of patients with eye disease. We present a state of the art eye exam which (1) reduces acuity exam error by 75\% without increasing exam length, (2) knows how confident it should be, (3) can trace predictions over time and incorporate prior beliefs and (4) provides insight for educational Item Response Theory. For patients with more serious eye disease, the novel ability to finely measure acuity from home could be a crucial part in early diagnosis. We provide a web implementation of our algorithm for anyone in the world to use.

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to make unbiased weight updates to a variance network. Further, we formulate a heuristic for robustly fitting both the mean and variance networks post hoc. Finally, we take inspiration from posterior Gaussian processes and propose a network architecture with similar extrapolation properties to Gaussian processes. The proposed methodologies are complementary, and improve upon baseline methods individually. Experimentally, we investigate the impact on predictive uncertainty on multiple datasets and tasks ranging from regression, active learning and generative modeling. Experiments consistently show significant improvements in predictive uncertainty estimation over state-of-the-art methods across tasks and datasets.

One major challenge for the legacy measurements at the LHC is that the likelihood function is not tractable when the collected data is high-dimensional and the detector response has to be modeled. We review how different analysis strategies solve this issue, including the traditional histogram approach used in most particle physics analyses, the Matrix Element Method, Optimal Observables, and modern techniques based on neural density estimation. We then discuss powerful new inference methods that use a combination of matrix element information and machine learning to accurately estimate the likelihood function. The MadMiner package automates all necessary data-processing steps. In first studies we find that these new techniques have the potential to substantially improve the sensitivity of the LHC legacy measurements.