Machine Learning (stat.ML)

Abstract: Even though dropout is a popular regularization technique, its theoretical properties are not fully understood. In this paper we study dropout regularization in extended generalized linear models based on double exponential families, for which the dispersion parameter can vary with the features. A theoretical analysis shows that dropout regularization prefers rare but important features in both the mean and dispersion, generalizing an earlier result for conventional generalized linear models. Training is performed using stochastic gradient descent with adaptive learning rate. To illustrate, we apply dropout to adaptive smoothing with B-splines, where both the mean and dispersion parameters are modelled flexibly. The important B-spline basis functions can be thought of as rare features, and we confirm in experiments that dropout is an effective form of regularization for mean and dispersion parameters that improves on a penalized maximum likelihood approach with an explicit smoothness penalty.

Abstract: Neural ordinary differential equations (neural ODEs) are a popular family of continuous-depth deep learning models. In this work, we consider a large family of parameterized ODEs with continuous-in-time parameters, which include time-dependent neural ODEs. We derive a generalization bound for this class by a Lipschitz-based argument. By leveraging the analogy between neural ODEs and deep residual networks, our approach yields in particular a generalization bound for a class of deep residual networks. The bound involves the magnitude of the difference between successive weight matrices. We illustrate numerically how this quantity affects the generalization capability of neural networks.

Abstract: In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for the robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, by using a sliding window approach. We then apply various clustering techniques (e.g, K-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are aggregated to enhance the identification of the consistent relationships in the original universe. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.

Abstract: Treatment effect estimation is of high-importance for both researchers and practitioners across many scientific and industrial domains. The abundance of observational data makes them increasingly used by researchers for the estimation of causal effects. However, these data suffer from biases, from several weaknesses, leading to inaccurate causal effect estimations, if not handled properly. Therefore, several machine learning techniques have been proposed, most of them focusing on leveraging the predictive power of neural network models to attain more precise estimation of causal effects. In this work, we propose a new methodology, named Nearest Neighboring Information for Causal Inference (NNCI), for integrating valuable nearest neighboring information on neural network-based models for estimating treatment effects. The proposed NNCI methodology is applied to some of the most well established neural network-based models for treatment effect estimation with the use of observational data. Numerical experiments and analysis provide empirical and statistical evidence that the integration of NNCI with state-of-the-art neural network models leads to considerably improved treatment effect estimations on a variety of well-known challenging benchmarks.

Abstract: We propose a general framework for visualizing any intermediate embedding representation used by any neural survival analysis model. Our framework is based on so-called anchor directions in an embedding space. We show how to estimate these anchor directions using clustering or, alternatively, using user-supplied "concepts" defined by collections of raw inputs (e.g., feature vectors all from female patients could encode the concept "female"). For tabular data, we present visualization strategies that reveal how anchor directions relate to raw clinical features and to survival time distributions. We then show how these visualization ideas extend to handling raw inputs that are images. Our framework is built on looking at angles between vectors in an embedding space, where there could be "information loss" by ignoring magnitude information. We show how this loss results in a "clumping" artifact that appears in our visualizations, and how to reduce this information loss in practice.

Abstract: If $X,Y,Z$ denote sets of random variables, two different data sources may contain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that causal discovery can help inferring properties of the `unobserved joint distributions' $P_{X,Y,Z}$ or $P_{X,Z}$. The properties may be conditional independences (as in `integrative causal inference') or also quantitative statements about dependences. More generally, we define a learning scenario where the input is a subset of variables and the label is some statistical property of that subset. Sets of jointly observed variables define the training points, while unobserved sets are possible test points. To solve this learning task, we infer, as an intermediate step, a causal model from the observations that then entails properties of unobserved sets. Accordingly, we can define the VC dimension of a class of causal models and derive generalization bounds for the predictions. Here, causal discovery becomes more modest and better accessible to empirical tests than usual: rather than trying to find a causal hypothesis that is `true' a causal hypothesis is {\it useful} whenever it correctly predicts statistical properties of unobserved joint distributions. This way, a sparse causal graph that omits weak influences may be more useful than a dense one (despite being less accurate) because it is able to reconstruct the full joint distribution from marginal distributions of smaller subsets. Within such a `pragmatic' application of causal discovery, some popular heuristic approaches become justified in retrospect. It is, for instance, allowed to infer DAGs from partial correlations instead of conditional independences if the DAGs are only used to predict partial correlations.