We study the problem of list-decodable linear regression, where an adversary can corrupt a majority of the examples. Specifically, we are given a set $T$ of labeled examples $(x, y) \in \mathbb{R}^d \times \mathbb{R}$ and a parameter $0< \alpha <1/2$ such that an $\alpha$-fraction of the points in $T$ are i.i.d. samples from a linear regression model with Gaussian covariates, and the remaining $(1-\alpha)$-fraction of the points are drawn from an arbitrary noise distribution. The goal is to output a small list of hypothesis vectors such that at least one of them is close to the target regression vector. Our main result is a Statistical Query (SQ) lower bound of $d^{\mathrm{poly}(1/\alpha)}$ for this problem. Our SQ lower bound qualitatively matches the performance of previously developed algorithms, providing evidence that current upper bounds for this task are nearly best possible.

We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. The SNICA setting therefore subsumes all the existing nonlinear ICA models for time-series and also allows for new much richer identifiable models. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

Nowadays new technologies, and especially artificial intelligence, are more and more established in our society. Big data analysis and machine learning, two sub-fields of artificial intelligence, are at the core of many recent breakthroughs in many application fields (e.g., medicine, communication, finance, ...), including some that are strongly related to our day-to-day life (e.g., social networks, computers, smartphones, ...). In machine learning, significant improvements are usually achieved at the price of an increasing computational complexity and thanks to bigger datasets. Currently, cutting-edge models built by the most advanced machine learning algorithms typically became simultaneously very efficient and profitable but also extremely complex. Their complexity is to such an extent that these models are commonly seen as black-boxes providing a prediction or a decision which can not be interpreted or justified. Nevertheless, whether these models are used autonomously or as a simple decision-making support tool, they are already being used in machine learning applications where health and human life are at stake. Therefore, it appears to be an obvious necessity not to blindly believe everything coming out of those models without a detailed understanding of their predictions or decisions. Accordingly, this thesis aims at improving the interpretability of models built by a specific family of machine learning algorithms, the so-called tree-based methods. Several mechanisms have been proposed to interpret these models and we aim along this thesis to improve their understanding, study their properties, and define their limitations.

Machine learning systems based on minimizing average error have been shown to perform inconsistently across notable subsets of the data, which is not exposed by a low average error for the entire dataset. In consequential social and economic applications, where data represent people, this can lead to discrimination of underrepresented gender and ethnic groups. Given the importance of bias mitigation in machine learning, the topic leads to contentious debates on how to ensure fairness in practice (data bias versus algorithmic bias). Distributionally Robust Optimization (DRO) seemingly addresses this problem by minimizing the worst expected risk across subpopulations. We establish theoretical results that clarify the relation between DRO and the optimization of the same loss averaged on an adequately weighted training dataset. The results cover finite and infinite number of training distributions, as well as convex and non-convex loss functions. We show that neither DRO nor curating the training set should be construed as a complete solution for bias mitigation: in the same way that there is no universally robust training set, there is no universal way to setup a DRO problem and ensure a socially acceptable set of results. We then leverage these insights to provide a mininal set of practical recommendations for addressing bias with DRO. Finally, we discuss ramifications of our results in other related applications of DRO, using an example of adversarial robustness. Our results show that there is merit to both the algorithm-focused and the data-focused side of the bias debate, as long as arguments in favor of these positions are precisely qualified and backed by relevant mathematics known today.

Kernel-based feature selection is an important tool in nonparametric statistics. Despite many practical applications of kernel-based feature selection, there is little statistical theory available to support the method. A core challenge is the objective function of the optimization problems used to define kernel-based feature selection are nonconvex. The literature has only studied the statistical properties of the \emph{global optima}, which is a mismatch, given that the gradient-based algorithms available for nonconvex optimization are only able to guarantee convergence to local minima. Studying the full landscape associated with kernel-based methods, we show that feature selection objectives using the Laplace kernel (and other $\ell_1$ kernels) come with statistical guarantees that other kernels, including the ubiquitous Gaussian kernel (or other $\ell_2$ kernels) do not possess. Based on a sharp characterization of the gradient of the objective function, we show that $\ell_1$ kernels eliminate unfavorable stationary points that appear when using an $\ell_2$ kernel. Armed with this insight, we establish statistical guarantees for $\ell_1$ kernel-based feature selection which do not require reaching the global minima. In particular, we establish model-selection consistency of $\ell_1$-kernel-based feature selection in recovering main effects and hierarchical interactions in the nonparametric setting with $n \sim \log p$ samples.

Multiple views of data, both naturally acquired (e.g., image and audio) and artificially produced (e.g., via adding different noise to data samples), have proven useful in enhancing representation learning. Natural views are often handled by multiview analysis tools, e.g., (deep) canonical correlation analysis [(D)CCA], while the artificial ones are frequently used in self-supervised learning (SSL) paradigms, e.g., SimCLR and Barlow Twins. Both types of approaches often involve learning neural feature extractors such that the embeddings of data exhibit high cross-view correlations. Although intuitive, the effectiveness of correlation-based neural embedding is only empirically validated. This work puts forth a theory-backed framework for unsupervised multiview learning. Our development starts with proposing a multiview model, where each view is a nonlinear mixture of shared and private components. Consequently, the learning problem boils down to shared/private component identification and disentanglement. Under this model, latent correlation maximization is shown to guarantee the extraction of the shared components across views (up to certain ambiguities). In addition, the private information in each view can be provably disentangled from the shared using proper regularization design. The method is tested on a series of tasks, e.g., downstream clustering, which all show promising performance. Our development also provides a unifying perspective for understanding various DCCA and SSL schemes.

Dot product latent space embedding is a common form of representation learning in undirected graphs (e.g. social networks, co-occurrence networks). We show that such models have problems dealing with 'intransitive' situations where A is linked to B, B is linked to C but A is not linked to C. Such situations occur in social networks when opposites attract (heterophily) and in co-occurrence networks when there are substitute nodes (e.g. the presence of Pepsi or Coke, but rarely both, in otherwise similar purchase baskets). We present a simple expansion which we call the attract-repel (AR) decomposition: a set of latent attributes on which similar nodes attract and another set of latent attributes on which similar nodes repel. We demonstrate the AR decomposition in real social networks and show that it can be used to measure the amount of latent homophily and heterophily. In addition, it can be applied to co-occurrence networks to discover roles in teams and find substitutable ingredients in recipes.

Federated learning involves training machine learning models over devices or data silos, such as edge processors or data warehouses, while keeping the data local. Training in heterogeneous and potentially massive networks introduces bias into the system, which is originated from the non-IID data and the low participation rate in reality. In this paper, we propose Elastic Federated Learning (EFL), an unbiased algorithm to tackle the heterogeneity in the system, which makes the most informative parameters less volatile during training, and utilizes the incomplete local updates. It is an efficient and effective algorithm that compresses both upstream and downstream communications. Theoretically, the algorithm has convergence guarantee when training on the non-IID data at the low participation rate. Empirical experiments corroborate the competitive performance of EFL framework on the robustness and the efficiency.

Prediction of survival in patients diagnosed with a brain tumour is challenging because of heterogeneous tumour behaviours and responses to treatment. Better estimations of prognosis would support treatment planning and patient support. Advances in machine learning have informed development of clinical predictive models, but their integration into clinical practice is almost non-existent. One reasons for this is the lack of interpretability of models. In this paper, we use a novel brain tumour dataset to compare two interpretable rule list models against popular machine learning approaches for brain tumour survival prediction. All models are quantitatively evaluated using standard performance metrics. The rule lists are also qualitatively assessed for their interpretability and clinical utility. The interpretability of the black box machine learning models is evaluated using two post-hoc explanation techniques, LIME and SHAP. Our results show that the rule lists were only slightly outperformed by the black box models. We demonstrate that rule list algorithms produced simple decision lists that align with clinical expertise. By comparison, post-hoc interpretability methods applied to black box models may produce unreliable explanations of local model predictions. Model interpretability is essential for understanding differences in predictive performance and for integration into clinical practice.

Attention mechanism enables the Graph Neural Networks(GNNs) to learn the attention weights between the target node and its one-hop neighbors, the performance is further improved. However, the most existing GNNs are oriented to homogeneous graphs and each layer can only aggregate the information of one-hop neighbors. Stacking multi-layer networks will introduce a lot of noise and easily lead to over smoothing. We propose a Multi-hop Heterogeneous Neighborhood information Fusion graph representation learning method (MHNF). Specifically, we first propose a hybrid metapath autonomous extraction model to efficiently extract multi-hop hybrid neighbors. Then, we propose a hop-level heterogeneous Information aggregation model, which selectively aggregates different-hop neighborhood information within the same hybrid metapath. Finally, a hierarchical semantic attention fusion model (HSAF) is proposed, which can efficiently integrate different-hop and different-path neighborhood information respectively. This paper can solve the problem of aggregating the multi-hop neighborhood information and can learn hybrid metapaths for target task, reducing the limitation of manually specifying metapaths. In addition, HSAF can extract the internal node information of the metapaths and better integrate the semantic information of different levels. Experimental results on real datasets show that MHNF is superior to state-of-the-art methods in node classification and clustering tasks (10.94% - 69.09% and 11.58% - 394.93% relative improvement on average, respectively).