Convergence of Manifold Filter-Combine Networks

In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). The filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and naturally suggests many interesting families of MNNs which can be interpreted as the manifold analog of various popular GNNs. We then propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating the manifold by a sparse graph. We prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity.

Atom-Level Optical Chemical Structure Recognition with Limited Supervision

Identifying the chemical structure from a graphical representation, or image, of a molecule is a challenging pattern recognition task that would greatly benefit drug development. Yet, existing methods for chemical structure recognition do not typically generalize well, and show diminished effectiveness when confronted with domains where data is sparse, or costly to generate, such as hand-drawn molecule images. To address this limitation, we propose a new chemical structure recognition tool that delivers state-of-the-art performance and can adapt to new domains with a limited number of data samples and supervision. Unlike previous approaches, our method provides atom-level localization, and can therefore segment the image into the different atoms and bonds. Our model is the first model to perform OCSR with atom-level entity detection with only SMILES supervision. Through rigorous and extensive benchmarking, we demonstrate the preeminence of our chemical structure recognition approach in terms of data efficiency, accuracy, and atom-level entity prediction.

Benchmarking Observational Studies with Experimental Data under Right-Censoring

Drawing causal inferences from observational studies (OS) requires unverifiable validity assumptions; however, one can falsify those assumptions by benchmarking the OS with experimental data from a randomized controlled trial (RCT). A major limitation of existing procedures is not accounting for censoring, despite the abundance of RCTs and OSes that report right-censored time-to-event outcomes. We consider two cases where censoring time (1) is independent of time-to-event and (2) depends on time-to-event the same way in OS and RCT. For the former, we adopt a censoring-doubly-robust signal for the conditional average treatment effect (CATE) to facilitate an equivalence test of CATEs in OS and RCT, which serves as a proxy for testing if the validity assumptions hold. For the latter, we show that the same test can still be used even though unbiased CATE estimation may not be possible. We verify the effectiveness of our censoring-aware tests via semi-synthetic experiments and analyze RCT and OS data from the Women's Health Initiative study.

BLIS-Net: Classifying and Analyzing Signals on Graphs

Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred to as signals) defined on the vertices of a single graph. These tasks require networks designed differently from those designed for traditional GNN tasks. Indeed, traditional GNNs rely on localized low-pass filters, and signals of interest may have intricate multi-frequency behavior and exhibit long range interactions. This motivates us to introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. Our network is able to capture both local and global signal structure and is able to capture both low-frequency and high-frequency information. We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data.

Manifold Filter-Combine Networks

We introduce a class of manifold neural networks (MNNs) that we call Manifold Filter-Combine Networks (MFCNs), that aims to further our understanding of MNNs, analogous to how the aggregate-combine framework helps with the understanding of graph neural networks (GNNs). This class includes a wide variety of subclasses that can be thought of as the manifold analog of various popular GNNs. We then consider a method, based on building a data-driven graph, for implementing such networks when one does not have global knowledge of the manifold, but merely has access to finitely many sample points. We provide sufficient conditions for the network to provably converge to its continuum limit as the number of sample points tends to infinity. Unlike previous work (which focused on specific graph constructions), our rate of convergence does not directly depend on the number of filters used. Moreover, it exhibits linear dependence on the depth of the network rather than the exponential dependence obtained previously. Additionally, we provide several examples of interesting subclasses of MFCNs and of the rates of convergence that are obtained under specific graph constructions.

Inferring dynamic regulatory interaction graphs from time series data with perturbations

Complex systems are characterized by intricate interactions between entities that evolve dynamically over time. Accurate inference of these dynamic relationships is crucial for understanding and predicting system behavior. In this paper, we propose Regulatory Temporal Interaction Network Inference (RiTINI) for inferring time-varying interaction graphs in complex systems using a novel combination of space-and-time graph attentions and graph neural ordinary differential equations (ODEs). RiTINI leverages time-lapse signals on a graph prior, as well as perturbations of signals at various nodes in order to effectively capture the dynamics of the underlying system. This approach is distinct from traditional causal inference networks, which are limited to inferring acyclic and static graphs. In contrast, RiTINI can infer cyclic, directed, and time-varying graphs, providing a more comprehensive and accurate representation of complex systems. The graph attention mechanism in RiTINI allows the model to adaptively focus on the most relevant interactions in time and space, while the graph neural ODEs enable continuous-time modeling of the system's dynamics. We evaluate RiTINI's performance on various simulated and real-world datasets, demonstrating its state-of-the-art capability in inferring interaction graphs compared to previous methods.

A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances. In this process, we also formulate a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. This novel perspective makes clearer the choices available in manifold learning and denoising. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances, and preserving cluster structure in toy datasets. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure, where our method enables interpolation of withheld timepoints of data. Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).

Weakly Supervised Knowledge Transfer with Probabilistic Logical Reasoning for Object Detection

Training object detection models usually requires instance-level annotations, such as the positions and labels of all objects present in each image. Such supervision is unfortunately not always available and, more often, only image-level information is provided, also known as weak supervision. Recent works have addressed this limitation by leveraging knowledge from a richly annotated domain. However, the scope of weak supervision supported by these approaches has been very restrictive, preventing them to use all available information. In this work, we propose ProbKT, a framework based on probabilistic logical reasoning that allows to train object detection models with arbitrary types of weak supervision. We empirically show on different datasets that using all available information is beneficial as our ProbKT leads to significant improvement on target domain and better generalization compared to existing baselines. We also showcase the ability of our approach to handle complex logic statements as supervision signal.

Anamnesic Neural Differential Equations with Orthogonal Polynomial Projections

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying dynamical system where new observations at arbitrary time points can be used to update the latent representation of the dynamical system. Existing parameterizations for the dynamics functions of Neural ODEs limit the ability of the model to retain global information about the time series; specifically, a piece-wise integration of the latent process between observations can result in a loss of memory on the dynamic patterns of previously observed data points. We propose PolyODE, a Neural ODE that models the latent continuous-time process as a projection onto a basis of orthogonal polynomials. This formulation enforces long-range memory and preserves a global representation of the underlying dynamical system. Our construction is backed by favourable theoretical guarantees and in a series of experiments, we demonstrate that it outperforms previous works in the reconstruction of past and future data, and in downstream prediction tasks.

Learning predictive checklists from continuous medical data

Checklists, while being only recently introduced in the medical domain, have become highly popular in daily clinical practice due to their combined effectiveness and great interpretability. Checklists are usually designed by expert clinicians that manually collect and analyze available evidence. However, the increasing quantity of available medical data is calling for a partially automated checklist design. Recent works have taken a step in that direction by learning predictive checklists from categorical data. In this work, we propose to extend this approach to accomodate learning checklists from continuous medical data using mixed-integer programming approach. We show that this extension outperforms a range of explainable machine learning baselines on the prediction of sepsis from intensive care clinical trajectories.