In practical applications, one often does not know the "true" structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal nonparametric screening methods have been recently developed. However, these approaches may miss important covariates that are marginally independent of the response, or may select unimportant covariates due to their high correlations with important covariates. To mitigate such shortcomings, we develop a conditional nonparametric quantile screening procedure (complemented by subsequent selection) for nonparametric additive quantile regression models. Under some mild conditions, we show that the proposed screening method can identify all relevant covariates in a small number of steps with probability approaching one. The subsequent narrowed best subset (via a modified Bayesian information criterion) also contains all the relevant covariates with overwhelming probability. The advantages of our proposed procedure are demonstrated through simulation studies and a real data example.
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Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyper-parameters. The newly proposed grid spectral mixture (GSM) kernel is tailored for multi-dimensional data, effectively reducing the number of hyper-parameters while maintaining good approximation capabilities. We further demonstrate that the associated hyper-parameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity property of the solutions, we introduce the Sparse LInear Multiple Kernel Learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMM) scheme for collaborative learning among multiple agents, where the local optimization problem is solved using a distributed successive convex approximation (DSCA) algorithm. SLIM-KL effectively manages large-scale hyper-parameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. Theoretical analysis establishes convergence guarantees for the learning framework, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our proposed methods.
Complex evidence theory, as a generalized D-S evidence theory, has attracted academic attention because it can well express uncertainty by means of complex basic belief assignment (CBBA), and realize uncertainty reasoning by complex combination rule. However, the uncertainty measurement in complex evidence theory is still an open issue. In order to make better decisions, a complex pignistic belief transformation (CPBT) method has been proposed to assign CBBAs of multi-element focal elements to subsets. The essence of CPBT is the redistribution of complex mass function by means of the concept of fractal. In this paper, based on fractal theory, experimental simulation and analysis have been carried out on the generation process of CPBT in time dimension. Then, a new fractal-based complex belief (FCB) entropy is proposed to measure the uncertainty of CBBA. Finally, the properties of FCB entropy are analyzed, and several examples are used to verify its effectiveness.
Generalization and sample efficiency have been long-standing issues concerning reinforcement learning, and thus the field of Offline Meta-Reinforcement Learning~(OMRL) has gained increasing attention due to its potential of solving a wide range of problems with static and limited offline data. Existing OMRL methods often assume sufficient training tasks and data coverage to apply contrastive learning to extract task representations. However, such assumptions are not applicable in several real-world applications and thus undermine the generalization ability of the representations. In this paper, we consider OMRL with two types of data limitations: limited training tasks and limited behavior diversity and propose a novel algorithm called GENTLE for learning generalizable task representations in the face of data limitations. GENTLE employs Task Auto-Encoder~(TAE), which is an encoder-decoder architecture to extract the characteristics of the tasks. Unlike existing methods, TAE is optimized solely by reconstruction of the state transition and reward, which captures the generative structure of the task models and produces generalizable representations when training tasks are limited. To alleviate the effect of limited behavior diversity, we consistently construct pseudo-transitions to align the data distribution used to train TAE with the data distribution encountered during testing. Empirically, GENTLE significantly outperforms existing OMRL methods on both in-distribution tasks and out-of-distribution tasks across both the given-context protocol and the one-shot protocol.
Private computation of nonlinear functions, such as Rectified Linear Units (ReLUs) and max-pooling operations, in deep neural networks (DNNs) poses significant challenges in terms of storage, bandwidth, and time consumption. To address these challenges, there has been a growing interest in utilizing privacy-preserving techniques that leverage polynomial activation functions and kernelized convolutions as alternatives to traditional ReLUs. However, these alternative approaches often suffer from a trade-off between achieving faster private inference (PI) and sacrificing model accuracy. In particular, when applied to much deeper networks, these methods encounter training instabilities, leading to issues like exploding gradients (resulting in NaNs) or suboptimal approximations. In this study, we focus on PolyKervNets, a technique known for offering improved dynamic approximations in smaller networks but still facing instabilities in larger and more complex networks. Our primary objective is to empirically explore optimization-based training recipes to enhance the performance of PolyKervNets in larger networks. By doing so, we aim to potentially eliminate the need for traditional nonlinear activation functions, thereby advancing the state-of-the-art in privacy-preserving deep neural network architectures. Code can be found on GitHub at: \url{//github.com/tolusophy/PolyKervNets/}
Gaussian process state-space models (GPSSMs) are a flexible and principled approach for modeling dynamical systems. However, existing variational learning and inference methods for GPSSMs often necessitate optimizing a substantial number of variational distribution parameters, leading to inadequate performance and efficiency. To overcome this issue, we propose incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the variational inference framework to approximate the posterior distribution of latent states. This utilization of EnKF can effectively exploit the dependencies between latent states and GP dynamics, while eliminating the need for parameterizing the variational distribution, thereby significantly reducing the number of variational parameters. Moreover, we show that our proposed algorithm allows straightforward evaluation of an approximated evidence lower bound (ELBO) in variational inference via simply summating multiple terms with readily available closed-form solutions. Leveraging automatic differentiation tools, we hence can maximize the ELBO and train the GPSSM efficiently. We also extend the proposed algorithm to an online setting and provide detailed algorithmic analyses and insights. Extensive evaluation on diverse real and synthetic datasets demonstrates the superiority of our EnKF-aided variational inference algorithms in terms of learning and inference performance compared to existing methods.
In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation has been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimation and belief estimation have only been tackled individually, which prevents existing methods from scaling to many agents. Therefore, we address these challenges simultaneously. First, we introduce weighted particle filtering to a sample-based online planner for MPOMDPs. Second, we present a scalable approximation of the belief. Third, we bring an approach that exploits the typical locality of agent interactions to novel online planning algorithms for MPOMDPs operating on a so-called sparse particle filter tree. Our experimental evaluation against several state-of-the-art baselines shows that our methods (1) are competitive in settings with only a few agents and (2) improve over the baselines in the presence of many agents.
This research explores a novel approach in the realm of learning-based image registration, addressing the limitations inherent in weakly-supervised and unsupervised methods. Weakly-supervised techniques depend heavily on scarce labeled data, while unsupervised strategies rely on indirect measures of accuracy through image similarity. Notably, traditional supervised learning is not utilized due to the lack of precise deformation ground-truth in medical imaging. Our study introduces a unique training framework with On-the-Fly Guidance (OFG) to enhance existing models. This framework, during training, generates pseudo-ground truth a few steps ahead by refining the current deformation prediction with our custom optimizer. This pseudo-ground truth then serves to directly supervise the model in a supervised learning context. The process involves optimizing the predicted deformation with a limited number of steps, ensuring training efficiency and setting achievable goals for each training phase. OFG notably boosts the precision of existing image registration techniques while maintaining the speed of learning-based methods. We assessed our approach using various pseudo-ground truth generation strategies, including predictions and optimized outputs from established registration models. Our experiments spanned three benchmark datasets and three cutting-edge models, with OFG demonstrating significant and consistent enhancements, surpassing previous state-of-the-arts in the field. OFG offers an easily integrable plug-and-play solution to enhance the training effectiveness of learning-based image registration models. Code at //github.com/miraclefactory/on-the-fly-guidance.
We study the use of a deep Gaussian process (DGP) prior in a general nonlinear inverse problem satisfying certain regularity conditions. We prove that when the data arises from a true parameter $\theta^*$ with a compositional structure, the posterior induced by the DGP prior concentrates around $\theta^*$ as the number of observations increases. The DGP prior accounts for the unknown compositional structure through the use of a hierarchical structure prior. As examples, we show that our results apply to Darcy's problem of recovering the scalar diffusivity from a steady-state heat equation and the problem of determining the attenuation potential in a steady-state Schr\"{o}dinger equation. We further provide a lower bound, proving in Darcy's problem that typical Gaussian priors based on Whittle-Mat\'{e}rn processes (which ignore compositional structure) contract at a polynomially slower rate than the DGP prior for certain diffusivities arising from a generalised additive model.
The simulation of plasma physics is computationally expensive because the underlying physical system is of high dimensions, requiring three spatial dimensions and three velocity dimensions. One popular numerical approach is Particle-In-Cell (PIC) methods owing to its ease of implementation and favorable scalability in high-dimensional problems. An unfortunate drawback of the method is the introduction of statistical noise resulting from the use of finitely many particles. In this paper we examine the application of the Smoothness-Increasing Accuracy-Conserving (SIAC) family of convolution kernel filters as denoisers for moment data arising from PIC simulations. We show that SIAC filtering is a promising tool to denoise PIC data in the physical space as well as capture the appropriate scales in the Fourier space. Furthermore, we demonstrate how the application of the SIAC technique reduces the amount of information necessary in the computation of quantities of interest in plasma physics such as the Bohm speed.
Data augmentation, the artificial creation of training data for machine learning by transformations, is a widely studied research field across machine learning disciplines. While it is useful for increasing the generalization capabilities of a model, it can also address many other challenges and problems, from overcoming a limited amount of training data over regularizing the objective to limiting the amount data used to protect privacy. Based on a precise description of the goals and applications of data augmentation (C1) and a taxonomy for existing works (C2), this survey is concerned with data augmentation methods for textual classification and aims to achieve a concise and comprehensive overview for researchers and practitioners (C3). Derived from the taxonomy, we divided more than 100 methods into 12 different groupings and provide state-of-the-art references expounding which methods are highly promising (C4). Finally, research perspectives that may constitute a building block for future work are given (C5).
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