Andrew Jones

Aishwarya Mandyam, Didong Li, Jiayu Yao et al.

Inverse reinforcement learning (IRL) methods infer an agent's reward function using demonstrations of expert behavior. A Bayesian IRL approach models a distribution over candidate reward functions, capturing a degree of uncertainty in the inferred reward function. This is critical in some applications, such as those involving clinical data. Typically, Bayesian IRL algorithms require large demonstration datasets, which may not be available in practice. In this work, we incorporate existing domain-specific data to achieve better posterior concentration rates. We study a common setting in clinical and biological applications where we have access to expert demonstrations and known reward functions for a set of training tasks. Our aim is to learn the reward function of a new test task given limited expert demonstrations. Existing Bayesian IRL methods impose restrictions on the form of input data, thus limiting the incorporation of training task data. To better leverage information from training tasks, we introduce kernel density Bayesian inverse reinforcement learning (KD-BIRL). Our approach employs a conditional kernel density estimator, which uses the known reward functions of the training tasks to improve the likelihood estimation across a range of reward functions and demonstration samples. Our empirical results highlight KD-BIRL's faster concentration rate in comparison to baselines, particularly in low test task expert demonstration data regimes. Additionally, we are the first to provide theoretical guarantees of posterior concentration for a Bayesian IRL algorithm. Taken together, this work introduces a principled and theoretically grounded framework that enables Bayesian IRL to be applied across a variety of domains.

Andrew Jones, Nick Whiteley

We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved locations, subject to additive noise. This leads us away from the standard assumption of i.i.d. data to a setting in which the $n$ covariate vectors are exchangeable but not independent in general. Under an assumption of independence across dimensions, $4$-th order moment, and other regularity conditions, we obtain probabilistic bounds on a notion of predictive excess risk adapted to our random functional covariate setting, making use of recent results of Barzilai and Shamir. We derive convergence rates in regimes where $p$ grows suitably fast relative to $n$, illustrating interplay between ingredients of the model in determining convergence behaviour and the role of additive covariate noise in benign-overfitting.

Emma Ceccherini, Ian Gallagher, Andrew Jones et al.

Stability for dynamic network embeddings ensures that nodes behaving the same at different times receive the same embedding, allowing comparison of nodes in the network across time. We present attributed unfolded adjacency spectral embedding (AUASE), a stable unsupervised representation learning framework for dynamic networks in which nodes are attributed with time-varying covariate information. To establish stability, we prove uniform convergence to an associated latent position model. We quantify the benefits of our dynamic embedding by comparing with state-of-the-art network representation learning methods on four real attributed networks. To the best of our knowledge, AUASE is the only attributed dynamic embedding that satisfies stability guarantees without the need for ground truth labels, which we demonstrate provides significant improvements for link prediction and node classification.

Aishwarya Mandyam, Andrew Jones, Jiayu Yao et al.

Reinforcement learning (RL) is an effective framework for solving sequential decision-making tasks. However, applying RL methods in medical care settings is challenging in part due to heterogeneity in treatment response among patients. Some patients can be treated with standard protocols whereas others, such as those with chronic diseases, need personalized treatment planning. Traditional RL methods often fail to account for this heterogeneity, because they assume that all patients respond to the treatment in the same way (i.e., transition dynamics are shared). We introduce Compositional Fitted $Q$-iteration (CFQI), which uses a compositional task structure to represent heterogeneous treatment responses in medical care settings. A compositional task consists of several variations of the same task, each progressing in difficulty; solving simpler variants of the task can enable efficient solving of harder variants. CFQI uses a compositional $Q$-value function with separate modules for each task variant, allowing it to take advantage of shared knowledge while learning distinct policies for each variant. We validate CFQI's performance using a Cartpole environment and use CFQI to recommend electrolyte repletion for patients with and without renal disease. Our results demonstrate that CFQI is robust even in the presence of class imbalance, enabling effective information usage across patient sub-populations. CFQI exhibits great promise for clinical applications in scenarios characterized by known compositional structures.

Ian Gallagher, Andrew Jones, Patrick Rubin-Delanchy

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this open-ended remit, we argue that two types of stability in the spatio-temporal positioning of nodes are desirable: to assign the same position, up to noise, to nodes behaving similarly at a given time (cross-sectional stability) and a constant position, up to noise, to a single node behaving similarly across different times (longitudinal stability). Similarity in behaviour is defined formally using notions of exchangeability under a dynamic latent position network model. By showing how this model can be recast as a multilayer random dot product graph, we demonstrate that unfolded adjacency spectral embedding satisfies both stability conditions. We also show how two alternative methods, omnibus and independent spectral embedding, alternately lack one or the other form of stability.

Petr Kellnhofer, Lars Jebe, Andrew Jones et al.

Novel view synthesis is a challenging and ill-posed inverse rendering problem. Neural rendering techniques have recently achieved photorealistic image quality for this task. State-of-the-art (SOTA) neural volume rendering approaches, however, are slow to train and require minutes of inference (i.e., rendering) time for high image resolutions. We adopt high-capacity neural scene representations with periodic activations for jointly optimizing an implicit surface and a radiance field of a scene supervised exclusively with posed 2D images. Our neural rendering pipeline accelerates SOTA neural volume rendering by about two orders of magnitude and our implicit surface representation is unique in allowing us to export a mesh with view-dependent texture information. Thus, like other implicit surface representations, ours is compatible with traditional graphics pipelines, enabling real-time rendering rates, while achieving unprecedented image quality compared to other surface methods. We assess the quality of our approach using existing datasets as well as high-quality 3D face data captured with a custom multi-camera rig.

Didong Li, Andrew Jones, Barbara Engelhardt

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal component analysis (CPCA) was proposed for this setting. However, the lack of a formal probabilistic model makes it difficult to reason about CPCA and to tune its hyperparameter. In this work, we propose probabilistic contrastive principal component analysis (PCPCA), a model-based alternative to CPCA. We discuss how to set the hyperparameter in theory and in practice, and we show several of PCPCA's advantages over CPCA, including greater interpretability, uncertainty quantification and principled inference, robustness to noise and missing data, and the ability to generate data from the model. We demonstrate PCPCA's performance through a series of simulations and case-control experiments with datasets of gene expression, protein expression, and images.

Andrew Jones, Patrick Rubin-Delanchy

We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for jointly embedding the associated adjacency matrices, or submatrices thereof, into a suitable latent space. Theoretical results concerning the asymptotic behaviour of the node representations thus obtained are established, showing that after the application of a linear transformation these converge uniformly in the Euclidean norm to the latent positions with Gaussian error. Within this framework, we present a generalisation of the stochastic block model to a number of different multiple graph settings, and demonstrate the effectiveness of our joint embedding method through several statistical inference tasks in which we achieve comparable or better results than rival spectral methods. Empirical improvements in link prediction over single graph embeddings are exhibited in a cyber-security example.

Ian Gallagher, Andrew Jones, Anna Bertiger et al.

When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of different embeddings -- which can be on entirely different scales -- by how easy it is to distinguish communities, in an information-theoretic sense. For common types of weighted graphs, such as count networks or p-value networks, we find that transformations such as tempering or thresholding can be highly beneficial, both in theory and in practice.