In this paper, we study the asymptotical properties of least squares regularized regression with indefinite kernels in reproducing kernel Kre\u{\i}n spaces (RKKS). The classical approximation analysis cannot be directly applied to study its asymptotical behavior under the framework of learning theory as this problem is in essence non-convex and outputs stationary points. By introducing a bounded hyper-sphere constraint to such non-convex regularized risk minimization problem, we theoretically demonstrate that this problem has a globally optimal solution with a closed form on the sphere, which makes our approximation analysis feasible in RKKS. Accordingly, we modify traditional error decomposition techniques, prove convergence results for the introduced hypothesis error based on matrix perturbation theory, and derive learning rates of such regularized regression problem in RKKS. Under some conditions, the derived learning rates in RKKS are the same as that in reproducing kernel Hilbert spaces (RKHS), which is actually the first work on approximation analysis of regularized learning algorithms in RKKS.

Phase retrieval, the problem of reconstructing a signal from the (squared) magnitude of its Fourier (or any linear) transform, arises in many fields of science and engineering. Such a task is naturally involved in applications such as crystallography (Millane, 1990) and diffraction imaging (Bunk et al., 2007), where optical sensors are able to measure the intensity, but not the phase of a light wave. Due to the loss of phase information, the one-dimensional Fourier phase retrieval problem is ill-posed in general. Common approaches to overcome this ill-posedness include using prior information such as non-negativity, sparsity and the signal's magnitude (Fienup, 1982; Jaganathan et al., 2016), or introducing redundancy into the measurements by oversampling random Gaussian measurements or coded diffraction patterns (Candès et al., 2015; Chen and Candès, 2015). In many applications, the underlying signal is naturally sparse (Jaganathan et al., 2016). A wide range of algorithms has been devised for phase retrieval with a sparse signal, including alternating minimization (SparseAltMinPhase) (Netrapalli et al., 2015), non-convex optimization based approaches such as thresholded Wirtinger flow (TWF) (Cai et al., 2016), sparse truncated amplitude flow (SPARTA) (Wang et al., 2018), compressive reweighted amplitude flow (CRAF) (Zhang et al., 2018) and sparse Wirtinger flow (SWF) (Yuan et al., 2019), and convex relaxation methods such as compressive phase retrieval via lifting (CPRL) (Ohlsson et al., 2012) and SparsePhaseMax (Hand and Voroninski, 2016). Other approaches to sparse phase retrieval include the greedy algorithm GESPAR (Schechtman et al., 2014), an algorithm based on generalized

Model-informed precision dosing (MIPD) using therapeutic drug/biomarker monitoring offers the opportunity to significantly improve the efficacy and safety of drug therapies. Current strategies comprise model-informed dosing tables or are based on maximum a-posteriori estimates. These approaches, however, lack a quantification of uncertainty and/or consider only part of the available patient-specific information. We propose three novel approaches for MIPD employing Bayesian data assimilation (DA) and/or reinforcement learning (RL) to control neutropenia, the major dose-limiting side effect in anticancer chemotherapy. These approaches have the potential to substantially reduce the incidence of life-threatening grade 4 and subtherapeutic grade 0 neutropenia compared to existing approaches. We further show that RL allows to gain further insights by identifying patient factors that drive dose decisions. Due to its flexibility, the proposed combined DA-RL approach can easily be extended to integrate multiple endpoints or patient-reported outcomes, thereby promising important benefits for future personalized therapies.

The recent availability of massive volumes of data fosters the need to design computationally efficient algorithms for optimization in high dimensions. In large-scale machine learning, stochastic gradient descent algorithms are among the most effective optimization methods (Bottou, Curtis and Nocedal 2018). For general smooth convex functions, averaged SGD achieves the rate of convergence of O(1/ k) after k iterations (Nemirovski, Juditsky, Lan and Shapiro 2009). For strongly-convex functions, i.e. when the smallest eigenvalue of the Hessian matrix is bounded away from 0, the convergence rate after k iterations is O(1/k) (Nemirovski, Juditsky, Lan and Shapiro 2009). Variance-reduced SGD algorithms that optimize the sum of n convex functions are described in (Schmidt, Le Roux and Bach 2017, Shalev-Shwartz and Zhang 2013, Johnson and Zhang 2013), and related accelerated methods are analysed in (Shalev-Shwartz and Zhang 2014, Nitanda 2014, Lan and Zhou 2018, Scieur, dAspremont and Bach 2018). These methods enjoy linear convergence(a convergence rate that decreases exponentially with the number of iterations) in the strongly-convex case. For general smooth convex functions, the stochastic average gradient method (SAG) of Schmidt, Le Roux and Bach (2017) yields a convergence rate of O( n/k) after k iterations. This paper focuses on the least-squares regression, which often arises in scientific computing and data analysis, and is widely used for inference and prediction. Many of the modern machine learning techniques such as the logistic and ridge regressions, the lasso method and neural networks can be considered as extensions of the least-squares regression technique.

This paper presents a semisupervised system responses evaluations, easy-to-evaluate surrogate models learning framework for dimension reduction and have been utilized as substitutes for computationally expensive reliability analysis. An autoencoder is first adopted for mapping simulations or experiments. Popular choices for surrogate the high-dimensional space into a low-dimensional latent space, models in the literature include, support vector machines (SVM) which contains a distinguishable failure surface. Then a deep [4-7], Kriging models [8-10], and artificial neural networks [11-feedforward neural network (DFN) is utilized to learn the 14]. Given a set of training data, surrogate models can be mapping relationship and reconstruct the latent space, while the constructed and then MCS can be directly carried out for Gaussian process (GP) modeling technique is used to build the reliability analysis. Research efforts have been devoted to surrogate model of the transformed limit state function. During developing adaptive sampling strategies [15-18], which aim at the training process of the DFN, the discrepancy between the balancing the fidelity of the surrogate model and the costs of actual and reconstructed latent space is minimized through semisupervised function evaluations.

A practical shortcoming of deep neural networks is their specialization to a single task and domain. While recent techniques in domain adaptation and multi-domain learning enable the learning of more domain-agnostic features, their success relies on the presence of domain labels, typically requiring manual annotation and careful curation of datasets. Here we focus on a less explored, but more realistic case: learning from data from multiple domains, without access to domain annotations. In this scenario, standard model training leads to the overfitting of large domains, while disregarding smaller ones. We address this limitation via dynamic residual adapters, an adaptive gating mechanism that helps account for latent domains, coupled with an augmentation strategy inspired by recent style transfer techniques. Our proposed approach is examined on image classification tasks containing multiple latent domains, and we showcase its ability to obtain robust performance across these. Dynamic residual adapters significantly outperform off-the-shelf networks with much larger capacity, and can be incorporated seamlessly with existing architectures in an end-to-end manner.

Learning accurate drug representation is essential for tasks such as computational drug repositioning and prediction of drug side-effects. A drug hierarchy is a valuable source that encodes human knowledge of drug relations in a tree-like structure where drugs that act on the same organs, treat the same disease, or bind to the same biological target are grouped together. However, its utility in learning drug representations has not yet been explored, and currently described drug representations cannot place novel molecules in a drug hierarchy. Here, we develop a semi-supervised drug embedding that incorporates two sources of information: (1) underlying chemical grammar that is inferred from molecular structures of drugs and drug-like molecules (unsupervised), and (2) hierarchical relations that are encoded in an expert-crafted hierarchy of approved drugs (supervised). We use the Variational Auto-Encoder (VAE) framework to encode the chemical structures of molecules and use the knowledge-based drug-drug similarity to induce the clustering of drugs in hyperbolic space. The hyperbolic space is amenable for encoding hierarchical concepts. Both quantitative and qualitative results support that the learned drug embedding can accurately reproduce the chemical structure and induce the hierarchical relations among drugs. Furthermore, our approach can infer the pharmacological properties of novel molecules by retrieving similar drugs from the embedding space. We demonstrate that the learned drug embedding can be used to find new uses for existing drugs and to discover side-effects. We show that it significantly outperforms baselines in both tasks.

Robust Reinforcement Learning aims to find the optimal policy with some extent of robustness to environmental dynamics. Existing learning algorithms usually enable the robustness through disturbing the current state or simulating environmental parameters in a heuristic way, which lack quantified robustness to the system dynamics (i.e. transition probability). To overcome this issue, we leverage Wasserstein distance to measure the disturbance to the reference transition kernel. With Wasserstein distance, we are able to connect transition kernel disturbance to the state disturbance, i.e. reduce an infinite-dimensional optimization problem to a finite-dimensional risk-aware problem. Through the derived risk-aware optimal Bellman equation, we show the existence of optimal robust policies, provide a sensitivity analysis for the perturbations, and then design a novel robust learning algorithm--Wasserstein Robust Advantage Actor-Critic algorithm (WRAAC). The effectiveness of the proposed algorithm is verified in the Cart-Pole environment.

We propose a model to tackle classification tasks in the presence of very little training data. To this aim, we approximate the notion of exact match with a theoretically sound mechanism that computes a probability of matching in the input space. Importantly, the model learns to focus on elements of the input that are relevant for the task at hand; by leveraging highlighted portions of the training data, an error boosting technique guides the learning process. In practice, it increases the error associated with relevant parts of the input by a given factor. Remarkable results on text classification tasks confirm the benefits of the proposed approach in both balanced and unbalanced cases, thus being of practical use when labeling new examples is expensive. In addition, by inspecting its weights, it is often possible to gather insights on what the model has learned.

During cluster analysis domain experts and visual analysis are frequently relied on to identify the optimal clustering structure. This process tends to be adhoc, subjective and difficult to reproduce. This work shows how competency questions can be used to formalise expert knowledge and application requirements for context specific evaluation of a clustering application in the residential energy consumption sector. While cluster analysis is an established unsupervised machine learning technique, identifying the optimal set of clusters for a specific application requires extensive experimentation and domain knowledge. Cluster compactness and distinctness are two important attributes that characterise a good cluster set (Sarle et al., 1990) and different metrics, such as the Mean Index Adequacy (MIA), Davies-Bouldin Index (DBI) and the Silhouette Index have been proposed to measure cluster compactness and distinctness.