Machine Learning (stat.ML)

Abstract: We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.

Abstract: Energy-Based Models (EBMs) offer a versatile framework for modeling complex data distributions. However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method for scalable EBM training suffers from inconsistency issues, causing the energy model to learn a `noisy' data distribution. In this work, we propose an efficient sampling framework: (pseudo)-Gibbs sampling with moment matching, which enables effective sampling from the underlying clean model when given a `noisy' model that has been well-trained via DSM. We explore the benefits of our approach compared to related methods and demonstrate how to scale the method to high-dimensional datasets.

Abstract: Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph clustering algorithms can be used to detect groups of strongly connected vertices and to derive coarse-grained models. We define transfer operators such as the Koopman operator and the Perron-Frobenius operator on graphs, study their spectral properties, introduce Galerkin projections of these operators, and illustrate how reduced representations can be estimated from data. In particular, we show that spectral clustering of undirected graphs can be interpreted in terms of eigenfunctions of the Koopman operator and propose novel clustering algorithms for directed graphs based on generalized transfer operators. We demonstrate the efficacy of the resulting algorithms on several benchmark problems and provide different interpretations of clusters.

Abstract: We propose a new multimodal variational autoencoder that enables to generate from the joint distribution and conditionally to any number of complex modalities. The unimodal posteriors are conditioned on the Deep Canonical Correlation Analysis embeddings which preserve the shared information across modalities leading to more coherent cross-modal generations. Furthermore, we use Normalizing Flows to enrich the unimodal posteriors and achieve more diverse data generation. Finally, we propose to use a Product of Experts for inferring one modality from several others which makes the model scalable to any number of modalities. We demonstrate that our method improves likelihood estimates, diversity of the generations and in particular coherence metrics in the conditional generations on several datasets.

Abstract: Continuous normalizing flows are widely used in generative tasks, where a flow network transports from a data distribution $P$ to a normal distribution. A flow model that can transport from $P$ to an arbitrary $Q$, where both $P$ and $Q$ are accessible via finite samples, would be of various application interests, particularly in the recently developed telescoping density ratio estimation (DRE) which calls for the construction of intermediate densities to bridge between $P$ and $Q$. In this work, we propose such a ``Q-malizing flow'' by a neural-ODE model which is trained to transport invertibly from $P$ to $Q$ (and vice versa) from empirical samples and is regularized by minimizing the transport cost. The trained flow model allows us to perform infinitesimal DRE along the time-parametrized $\log$-density by training an additional continuous-time flow network using classification loss, which estimates the time-partial derivative of the $\log$-density. Integrating the time-score network along time provides a telescopic DRE between $P$ and $Q$ that is more stable than a one-step DRE. The effectiveness of the proposed model is empirically demonstrated on mutual information estimation from high-dimensional data and energy-based generative models of image data.