This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between generalisation bounds based on the regularity of the loss function, and their chained counterparts, which can be obtained by lifting the regularity assumption from the loss onto its gradient. This allows us to re-derive the chaining mutual information bound from the literature, and to obtain novel chained information-theoretic generalisation bounds, based on the Wasserstein distance and other probability metrics. We show on some toy examples that the chained generalisation bound can be significantly tighter than its standard counterpart, particularly when the distribution of the hypotheses selected by the algorithm is very concentrated.

Linear regression is both a statistical and a machine learning algorithm.

Digital health data are multimodal and high-dimensional. A patient’s health state can be characterized by a multitude of signals including medical imaging, clinical variables, genome sequencing, conversations between clinicians and patients, and continuous signals from wearables, among others. This high volume, personalized data stream aggregated over patients’ lives has spurred interest in developing new artificial intelligence (AI) models for higher-precision diagnosis, prognosis, and tracking. While the promise of these algorithms is undeniable, their dissemination and adoption have been slow, owing partially to unpredictable AI model performance once deployed in the real world. We posit that one of the rate-limiting factors in developing algorithms that generalize to real-world scenarios is the very attribute that makes the data exciting—their high-dimensional nature. This paper considers how the large number of features in vast digital health data can challenge the development of robust AI models—a phenomenon known as “the curse of dimensionality” in statistical learning theory. We provide an overview of the curse of dimensionality in the context of digital health, demonstrate how it can negatively impact out-of-sample performance, and highlight important considerations for researchers and algorithm designers.

The large majority of human activities require collaborations within and across formal or informal teams. Our understanding of how the collaborative efforts spent by teams relate to their performance is still a matter of debate. Teamwork results in a highly interconnected ecosystem of potentially overlapping components where tasks are performed in interaction with team members and across other teams. To tackle this problem, we propose a graph neural network model designed to predict a team's performance while identifying the drivers that determine such an outcome. In particular, the model is based on three architectural channels: topological, centrality, and contextual which capture different factors potentially shaping teams' success. We endow the model with two attention mechanisms to boost model performance and allow interpretability. A first mechanism allows pinpointing key members inside the team. A second mechanism allows us to quantify the contributions of the three driver effects in determining the outcome performance. We test model performance on a wide range of domains outperforming most of the classical and neural baselines considered. Moreover, we include synthetic datasets specifically designed to validate how the model disentangles the intended properties on which our model vastly outperforms baselines.

We study the problem of model selection in bandit scenarios in the presence of nested policy classes, with the goal of obtaining simultaneous adversarial and stochastic ("best of both worlds") high-probability regret guarantees. Our approach requires that each base learner comes with a candidate regret bound that may or may not hold, while our meta algorithm plays each base learner according to a schedule that keeps the base learner's candidate regret bounds balanced until they are detected to violate their guarantees. We develop careful mis-specification tests specifically designed to blend the above model selection criterion with the ability to leverage the (potentially benign) nature of the environment. We recover the model selection guarantees of the CORRAL [Agarwal et al., 2017] algorithm for adversarial environments, but with the additional benefit of achieving high probability regret bounds, specifically in the case of nested adversarial linear bandits. More importantly, our model selection results also hold simultaneously in stochastic environments under gap assumptions. These are the first theoretical results that achieve best of both world (stochastic and adversarial) guarantees while performing model selection in (linear) bandit scenarios.

Electromyography signals can be used as training data by machine learning models to classify various gestures. We seek to produce a model that can classify six different hand gestures with a limited number of samples that generalizes well to a wider audience while comparing the effect of our feature extraction results on model accuracy to other more conventional methods such as the use of AR parameters on a sliding window across the channels of a signal. We appeal to a set of more elementary methods such as the use of random bounds on a signal, but desire to show the power these methods can carry in an online setting where EMG classification is being conducted, as opposed to more complicated methods such as the use of the Fourier Transform. To augment our limited training data, we used a standard technique, known as jitter, where random noise is added to each observation in a channel wise manner. Once all datasets were produced using the above methods, we performed a grid search with Random Forest and XGBoost to ultimately create a high accuracy model. For human computer interface purposes, high accuracy classification of EMG signals is of particular importance to their functioning and given the difficulty and cost of amassing any sort of biomedical data in a high volume, it is valuable to have techniques that can work with a low amount of high-quality samples with less expensive feature extraction methods that can reliably be carried out in an online application.

Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is violated in many real-world datasets and applications centered on relational systems. This work examines the problem of estimating independence in data drawn from relational systems by defining sufficient representations for the sets of observations influencing individual instances. Specifically, we define marginal and conditional independence tests for relational data by considering the kernel mean embedding as a flexible aggregation function for relational variables. We propose a consistent, non-parametric, scalable kernel test to operationalize the relational independence test for non-i.i.d. observational data under a set of structural assumptions. We empirically evaluate our proposed method on a variety of synthetic and semi-synthetic networks and demonstrate its effectiveness compared to state-of-the-art kernel-based independence tests.

Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting different complexity notions such as the mutual information between the data sample and the algorithm output, compressibility of the hypothesis space, and the fractal dimension of the hypothesis space. While these bounds have illuminated the problem at hand from different angles, their suggested complexity notions might appear seemingly unrelated, thereby restricting their high-level impact. In this study, we prove novel generalization bounds through the lens of rate-distortion theory, and explicitly relate the concepts of mutual information, compressibility, and fractal dimensions in a single mathematical framework. Our approach consists of (i) defining a generalized notion of compressibility by using source coding concepts, and (ii) showing that the `compression error rate' can be linked to the generalization error both in expectation and with high probability. We show that in the `lossless compression' setting, we recover and improve existing mutual information-based bounds, whereas a `lossy compression' scheme allows us to link generalization to the rate-distortion dimension -- a particular notion of fractal dimension. Our results bring a more unified perspective on generalization and open up several future research directions.

We consider a general non-linear model where the signal is a finite mixture of an unknown, possibly increasing, number of features issued from a continuous dictionary parameterized by a real nonlinear parameter. The signal is observed with Gaussian (possibly correlated) noise in either a continuous or a discrete setup. We propose an off-the-grid optimization method, that is, a method which does not use any discretization scheme on the parameter space, to estimate both the non-linear parameters of the features and the linear parameters of the mixture. We use recent results on the geometry of off-the-grid methods to give minimal separation on the true underlying non-linear parameters such that interpolating certificate functions can be constructed. Using also tail bounds for suprema of Gaussian processes we bound the prediction error with high probability. Assuming that the certificate functions can be constructed, our prediction error bound is up to log --factors similar to the rates attained by the Lasso predictor in the linear regression model. We also establish convergence rates that quantify with high probability the quality of estimation for both the linear and the non-linear parameters.

In plant breeding the presence of a genotype by environment (GxE) interaction has a strong impact on cultivation decision making and the introduction of new crop cultivars. The combination of linear and bilinear terms has been shown to be very useful in modelling this type of data. A widely-used approach to identify GxE is the Additive Main Effects and Multiplicative Interaction Effects (AMMI) model. However, as data frequently can be high-dimensional, Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible. In this article, we consider a variational inference approach for such a model. We derive variational approximations for estimating the parameters and we compare the approximations to MCMC using both simulated and real data. The new inferential framework we propose is on average two times faster whilst maintaining the same predictive performance as MCMC.