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Many dynamical systems exhibit latent states with intrinsic orderings such as "ally", "neutral" and "enemy" relationships in international relations. Such latent states are evidenced through entities' cooperative versus conflictual interactions which are similarly ordered. Models of such systems often involve state-to-action emission and state-to-state transition matrices. It is common practice to assume that the rows of these stochastic matrices are independently sampled from a Dirichlet distribution. However, this assumption discards ordinal information and treats states and actions falsely as order-invariant categoricals, which hinders interpretation and evaluation. To address this problem, we propose the Ordered Matrix Dirichlet (OMD): rows are sampled conditionally dependent such that probability mass is shifted to the right of the matrix as we move down rows. This results in a well-ordered mapping between latent states and observed action types. We evaluate the OMD in two settings: a Hidden Markov Model and a novel Bayesian Dynamic Poisson Tucker Model tailored to political event data. Models built on the OMD recover interpretable latent states and show superior forecasting performance in few-shot settings. We detail the wide applicability of the OMD to other domains where models with Dirichlet-sampled matrices are popular (e.g. topic modeling) and publish user-friendly code.

We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and provides estimates of uncertainty, but we aim to include systems where there are discontinuities between the two output solutions. Due to continuity assumptions, we consider current methods of classification to split our input space into two output regions. Classification and logistic regression methods currently rely on drawing from an independent Bernoulli distribution, which neglects any information known in the neighbouring area. We build on this by including correlation between our input points. Gaussian processes are still a vital element, but used in latent space to model the two regions. Using the input values and an associated output class label, the latent variable is estimated using MCMC sampling and a unique likelihood. A threshold (usually at zero) defines the boundary. We apply our method to a motivating example provided by the hormones associated with the reproductive system in mammals, where the two solutions are associated with high and low rates of reproduction.

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on how weakly informative the disease measurements are, we offer a kind of `best case' as well as a `worst case' analysis where, in the former case, we assume that the prevalence is directly accessible, while in the latter that only a binary signal corresponding to a prevalence detection threshold is available. Both cases are studied under an assumed so-called linear noise approximation as to the true dynamics. Numerical experiments test the sharpness of our results when confronted with more realistic situations for which analytical results are unavailable.

The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be applied to handle random fields that are only locally stationary, i.e., they can be assumed to be stationary only across a limited part over their entire region of definition. We construct one-step-ahead point predictors and compare the performance of Model-free to Model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, Model-free and Model-based, are novel in the context of random fields that are locally (but not globally) stationary. We demonstrate the application of our Model-based and Model-free point prediction methods to synthetic data as well as images from the CIFAR-10 dataset and in the latter case show that our best Model-free point prediction results outperform those obtained using Model-based prediction.

We apply reinforcement learning (RL) to robotics. One of the drawbacks of traditional RL algorithms has been their poor sample efficiency. One approach to improve it is model-based RL. We learn a model of the environment, essentially its dynamics and reward function, use it to generate imaginary trajectories and backpropagate through them to update the policy, exploiting the differentiability of the model. Intuitively, learning more accurate models should lead to better performance. Recently, there has been growing interest in developing better deep neural network based dynamics models for physical systems, through better inductive biases. We focus on robotic systems undergoing rigid body motion. We compare two versions of our model-based RL algorithm, one which uses a standard deep neural network based dynamics model and the other which uses a much more accurate, physics-informed neural network based dynamics model. We show that, in environments that are not sensitive to initial conditions, model accuracy matters only to some extent, as numerical errors accumulate slowly. In these environments, both versions achieve similar average-return, while the physics-informed version achieves better sample efficiency. We show that, in environments that are sensitive to initial conditions, model accuracy matters a lot, as numerical errors accumulate fast. In these environments, the physics-informed version achieves significantly better average-return and sample efficiency. We show that, in challenging environments, where we need a lot of samples to learn, physics-informed model-based RL can achieve better asymptotic performance than model-free RL, by generating accurate imaginary data, which allows it to perform many more policy updates. In these environments, our physics-informed model-based RL approach achieves better average-return than Soft Actor-Critic, a SOTA model-free RL algorithm.

Off-policy evaluation (OPE) attempts to predict the performance of counterfactual policies using log data from a different policy. We extend its applicability by developing an OPE method for a class of both full support and deficient support logging policies in contextual-bandit settings. This class includes deterministic bandit (such as Upper Confidence Bound) as well as deterministic decision-making based on supervised and unsupervised learning. We prove that our method's prediction converges in probability to the true performance of a counterfactual policy as the sample size increases. We validate our method with experiments on partly and entirely deterministic logging policies. Finally, we apply it to evaluate coupon targeting policies by a major online platform and show how to improve the existing policy.

Neural networks leverage robust internal representations in order to generalise. Learning them is difficult, and often requires a large training set that covers the data distribution densely. We study a common setting where our task is not purely opaque. Indeed, very often we may have access to information about the underlying system (e.g. that observations must obey certain laws of physics) that any "tabula rasa" neural network would need to re-learn from scratch, penalising performance. We incorporate this information into a pre-trained reasoning module, and investigate its role in shaping the discovered representations in diverse self-supervised learning settings from pixels. Our approach paves the way for a new class of representation learning, grounded in algorithmic priors.

Visualizing medical histories of patients with complex chronic diseases (e.g., discordant chronic comorbidities (DCCs)) is a challenge for patients, their healthcare providers, and their support network. DCCs are health conditions in which patients have multiple, often unrelated, chronic illnesses that may need to be addressed concurrently but may also be associated with conflicting treatment instructions. Future work targeting to reduce treatment conflicts and improve patient quality of life and care should carefully examine and visualize DCCs medical reports, symptoms, and treatment recommendations. In this study, we explore various visualization models and paradigms. We analyze how these models and paradigms are applied to visualize multifaceted medical data. We then propose a model for transforming the unstructured data into temporal slices and depict them in a single graphic model. We report how we carefully moved multifaceted DCC records into; structured data tables, visualization graphs, and various hardware devices.

Physical Ising machines rely on nature to guide a dynamical system towards an optimal state which can be read out as a heuristical solution to a combinatorial optimization problem. Such designs that use nature as a computing mechanism can lead to higher performance and/or lower operation costs and hence have attracted research and prototyping efforts from industry and academia. Quantum annealers are a prominent example of such efforts. However, some physics-centric Ising machines require stringent operating conditions that result in significant bulk and energy budget. Such disadvantages may be acceptable if these designs provide some significant intrinsic advantages at a much larger scale in the future, which remains to be seen. But for now, integrated electronic designs of Ising machines allow more immediate applications. We propose one such design that uses bistable nodes, coupled with programmable and variable strengths. The design is fully CMOS compatible for chip-scale applications and demonstrates competitive solution quality and significantly superior execution time and energy.

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids (in Lagrangian descriptions). Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities. It is a potential alternative approach to understanding complex fluid mechanics, such as turbulence, that are difficult to model using traditional methods of mathematical physics.