Humans are expert explorers. Understanding the computational cognitive mechanisms that support this efficiency can advance the study of the human mind and enable more efficient exploration algorithms. We hypothesize that humans explore new environments efficiently by inferring the structure of unobserved spaces using spatial information collected from previously explored spaces. This cognitive process can be modeled computationally using program induction in a Hierarchical Bayesian framework that explicitly reasons about uncertainty with strong spatial priors. Using a new behavioral Map Induction Task, we demonstrate that this computational framework explains human exploration behavior better than non-inductive models and outperforms state-of-the-art planning algorithms when applied to a realistic spatial navigation domain.

Coupled dynamical systems are frequently observed in nature, but often not well understood in terms of their causal structure without additional domain knowledge about the system. Especially when analyzing observational time series data of dynamical systems where it is not possible to conduct controlled experiments, for example time series of climate variables, it can be challenging to determine how features causally influence each other. There are many techniques available to recover causal relationships from data, such as Granger causality, convergent cross mapping, and causal graph structure learning approaches such as PCMCI. Path signatures and their associated signed areas provide a new way to approach the analysis of causally linked dynamical systems, particularly in informing a model-free, data-driven approach to algorithmic causal discovery. With this paper, we explore the use of path signatures in causal discovery and propose the application of confidence sequences to analyze the significance of the magnitude of the signed area between two variables. These confidence sequence regions converge with greater sampling length, and in conjunction with analyzing pairwise signed areas across time-shifted versions of the time series, can help identify the presence of lag/lead causal relationships. This approach provides a new way to define the confidence of a causal link existing between two time series, and ultimately may provide a framework for hypothesis testing to define whether one time series causes another.

A few-shot generative model should be able to generate data from a distribution by only observing a limited set of examples. In few-shot learning the model is trained on data from many sets from different distributions sharing some underlying properties such as sets of characters from different alphabets or sets of images of different type objects. We study a latent variables approach that extends the Neural Statistician [8] to a fully hierarchical approach with an attention-based point to set-level aggregation. We extend the previous work to iterative data sampling, likelihood-based model comparison, and adaptation-free out of distribution generalization. Our results show that the hierarchical formulation better captures the intrinsic variability within the sets in the small data regime. With this work we generalize deep latent variable approaches to few-shot learning, taking a step towards large-scale few-shot generation with a formulation that readily can work with current state-of-the-art deep generative models.

Roth (1996) proved that any form of marginal inference with probabilistic graphical models (e.g. Bayesian Networks) will at least be NP-hard. Introduced and extensively investigated in the past decade, the neural probabilistic circuits known as sum-product network (SPN) offers linear time complexity. On another note, research around neural causal models (NCM) recently gained traction, demanding a tighter integration of causality for machine learning. To this end, we present a theoretical investigation of if, when, how and under what cost tractability occurs for different NCM. We prove that SPN-based causal inference is generally tractable, opposed to standard MLP-based NCM. We further introduce a new tractable NCM-class that is efficient in inference and fully expressive in terms of Pearl's Causal Hierarchy. Our comparative empirical illustration on simulations and standard benchmarks validates our theoretical proofs.

With the widespread use of machine learning to support decision-making, it is increasingly important to verify and understand the reasons why a particular output is produced. Although post-training feature importance approaches assist this interpretation, there is an overall lack of consensus regarding how feature importance should be quantified, making explanations of model predictions unreliable. In addition, many of these explanations depend on the specific machine learning approach employed and on the subset of data used when calculating feature importance. A possible solution to improve the reliability of explanations is to combine results from multiple feature importance quantifiers from different machine learning approaches coupled with re-sampling. Current state-of-the-art ensemble feature importance fusion uses crisp techniques to fuse results from different approaches. There is, however, significant loss of information as these approaches are not context-aware and reduce several quantifiers to a single crisp output. More importantly, their representation of 'importance' as coefficients is misleading and incomprehensible to end-users and decision makers. Here we show how the use of fuzzy data fusion methods can overcome some of the important limitations of crisp fusion methods.

We propose a Bayesian approach for both medical inquiry and disease inference, the two major phases in differential diagnosis. Unlike previous work that simulates data from given probabilities and uses ML algorithms on them, we directly use the Quick Medical Reference (QMR) belief network, and apply Bayesian inference in the inference phase and Bayesian experimental design in the inquiry phase. Moreover, we improve the inquiry phase by extending the Bayesian experimental design framework from one-step search to multi-step search. Our approach has some practical advantages as it is interpretable, free of costly training, and able to adapt to new changes without any additional effort. Our experiments show that our approach achieves new state-of-the-art results on two simulated datasets, SymCAT and HPO, and competitive results on two diagnosis dialogue datasets, Muzhi and Dxy.

The growth of machine learning as a field has been accelerating with increasing interest and publications across fields, including statistics, but predominantly in computer science. How can we parse this vast literature for developments that exemplify the necessary rigor? How many of these manuscripts incorporate foundational theory to allow for statistical inference? Which advances have the greatest potential for impact in practice? One could posit many answers to these queries. Here, we assert that one essential idea is for machine learning to integrate maximum likelihood for estimation of functional parameters, such as prediction functions and conditional densities.

Recent studies have empirically investigated different methods to train a stochastic classifier by optimising a PAC-Bayesian bound via stochastic gradient descent. Most of these procedures need to replace the misclassification error with a surrogate loss, leading to a mismatch between the optimisation objective and the actual generalisation bound. The present paper proposes a novel training algorithm that optimises the PAC-Bayesian bound, without relying on any surrogate loss. Empirical results show that the bounds obtained with this approach are tighter than those found in the literature.

In vitro cellular experimentation with genetic interventions, using for example CRISPR technologies, is an essential step in early-stage drug discovery and target validation that serves to assess initial hypotheses about causal associations between biological mechanisms and disease pathologies. With billions of potential hypotheses to test, the experimental design space for in vitro genetic experiments is extremely vast, and the available experimental capacity - even at the largest research institutions in the world - pales in relation to the size of this biological hypothesis space. Machine learning methods, such as active and reinforcement learning, could aid in optimally exploring the vast biological space by integrating prior knowledge from various information sources as well as extrapolating to yet unexplored areas of the experimental design space based on available data. However, there exist no standardised benchmarks and data sets for this challenging task and little research has been conducted in this area to date. Here, we introduce GeneDisco, a benchmark suite for evaluating active learning algorithms for experimental design in drug discovery. GeneDisco contains a curated set of multiple publicly available experimental data sets as well as open-source implementations of state-of-the-art active learning policies for experimental design and exploration.

This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately, serially, and with black-box algorithms, which obscures the interactions between spatial and temporal approximation errors and misguides the quantification of the overall error. To fix this issue, we introduce a probabilistic version of a technique called method of lines. The proposed algorithm begins with a Gaussian process interpretation of finite difference methods, which then interacts naturally with filtering-based probabilistic ordinary differential equation (ODE) solvers because they share a common language: Bayesian inference. Joint quantification of space- and time-uncertainty becomes possible without losing the performance benefits of well-tuned ODE solvers. Thereby, we extend the toolbox of probabilistic programs for differential equation simulation to PDEs.