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The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new approach is proposed to train SVC and optimize the selection of Gaussian kernel parameters. We first formulate the training and parameter selection of SVC as a minimax optimization problem named as MaxMin-L2-SVC-NCH, in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal Gaussian kernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is not needed. We then propose a projected gradient algorithm (PGA) for training L2-SVC-NCH. The famous sequential minimal optimization (SMO) algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility than the SMO. Furthermore, the solution of the maximization problem is done by a gradient ascent algorithm with dynamic learning rate. The comparative experiments between MaxMin-L2-SVC-NCH and the previous best approaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained while maintaining competitive test accuracy. These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVC tasks.

The widespread adoption of distributed learning to train a global model from local data has been hindered by the challenge posed by stragglers. Recent attempts to mitigate this issue through gradient coding have proved difficult due to the large amounts of data redundancy, computational and communicational overhead it brings. Additionally, the complexity of encoding and decoding increases linearly with the number of local workers. In this paper, we present a lightweight coding method for the computing phase and a fair transmission protocol for the communication phase, to mitigate the straggler problem. A two-stage dynamic coding scheme is proposed for the computing phase, where partial gradients are computed by a portion of workers in the first stage and the remainder are decided based on their completion status in the first stage. To ensure fair communication, a perturbed Lyapunov function is designed to balance admission data fairness and maximize throughput. Extensive experimental results demonstrate the superiority of our proposed solution in terms of accuracy and resource utilization in the distributed learning system, even under practical network conditions and benchmark data.

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and might lead to a suboptimal solution to the original problem. In addition, the intermediate solutions, often ignored by classic homotopy optimization, could be useful for many real-world applications. In this work, we propose a novel model-based approach to learn the whole continuation path for homotopy optimization, which contains infinite intermediate solutions for any surrogate subproblems. Rather than the classic unidirectional easy-to-hard optimization, our method can simultaneously optimize the original problem and all surrogate subproblems in a collaborative manner. The proposed model also supports real-time generation of any intermediate solution, which could be desirable for many applications. Experimental studies on different problems show that our proposed method can significantly improve the performance of homotopy optimization and provide extra helpful information to support better decision-making.

Recommendation system algorithm based on multi-task learning (MTL) is the major method for Internet operators to understand users and predict their behaviors in the multi-behavior scenario of platform. Task correlation is an important consideration of MTL goals, traditional models use shared-bottom models and gating experts to realize shared representation learning and information differentiation. However, The relationship between real-world tasks is often more complex than existing methods do not handle properly sharing information. In this paper, we propose an Different Expression Parallel Heterogeneous Network (DEPHN) to model multiple tasks simultaneously. DEPHN constructs the experts at the bottom of the model by using different feature interaction methods to improve the generalization ability of the shared information flow. In view of the model's differentiating ability for different task information flows, DEPHN uses feature explicit mapping and virtual gradient coefficient for expert gating during the training process, and adaptively adjusts the learning intensity of the gated unit by considering the difference of gating values and task correlation. Extensive experiments on artificial and real-world datasets demonstrate that our proposed method can capture task correlation in complex situations and achieve better performance than baseline models\footnote{Accepted in IJCNN2023}.

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though we understand the sample complexity of learning a VC dimension d class on $k$ distributions to be $O(\epsilon^{-2} \ln(k)(d + k) + \min\{\epsilon^{-1} dk, \epsilon^{-4} \ln(k) d\})$, the best lower bound is $\Omega(\epsilon^{-2}(d + k \ln(k)))$. We discuss recent progress on this problem and some hurdles that are fundamental to the use of game dynamics in statistical learning.

In this paper, we use Prior-data Fitted Networks (PFNs) as a flexible surrogate for Bayesian Optimization (BO). PFNs are neural processes that are trained to approximate the posterior predictive distribution (PPD) through in-context learning on any prior distribution that can be efficiently sampled from. We describe how this flexibility can be exploited for surrogate modeling in BO. We use PFNs to mimic a naive Gaussian process (GP), an advanced GP, and a Bayesian Neural Network (BNN). In addition, we show how to incorporate further information into the prior, such as allowing hints about the position of optima (user priors), ignoring irrelevant dimensions, and performing non-myopic BO by learning the acquisition function. The flexibility underlying these extensions opens up vast possibilities for using PFNs for BO. We demonstrate the usefulness of PFNs for BO in a large-scale evaluation on artificial GP samples and three different hyperparameter optimization testbeds: HPO-B, Bayesmark, and PD1. We publish code alongside trained models at github.com/automl/PFNs4BO.

Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also an abductive explanation or a PI-explanation. The second type explains why some other decision was not made and is known as a necessary reason for the decision, also a contrastive or counterfactual explanation. These explanations were defined for classifiers with binary, discrete and, in some cases, continuous features. We show that these explanations can be significantly improved in the presence of non-binary features, leading to a new class of explanations that relay more information about decisions and the underlying classifiers. Necessary and sufficient reasons were also shown to be the prime implicates and implicants of the complete reason for a decision, which can be obtained using a quantification operator. We show that our improved notions of necessary and sufficient reasons are also prime implicates and implicants but for an improved notion of complete reason obtained by a new quantification operator that we also define and study.

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.