Gaussian Processes (GPs) are a versatile method that enables different approaches towards learning for dynamics and control. Gaussianity assumptions appear in two dimensions in GPs: The positive semi-definite kernel of the underlying reproducing kernel Hilbert space is used to construct the co-variance of a Gaussian distribution over functions, while measurement noise (i.e. data corruption) is usually modeled as i.i.d. additive Gaussian. In this note, we relax the latter Gaussianity assumption, i.e., we consider kernel ridge regression with additive i.i.d. non-Gaussian measurement noise. To apply the usual kernel trick, we rely on the representation of the uncertainty via polynomial chaos expansions, which are series expansions for random variables of finite variance introduced by Norbert Wiener. We derive and discuss the analytic $\mathcal{L}^2$ solution to the arising Wiener kernel regression. Considering a polynomial system as numerical example, we show that our approach allows to untangle the effects of epistemic and aleatoric uncertainties.
Self-supervised skill learning aims to acquire useful behaviors that leverage the underlying dynamics of the environment. Latent variable models, based on mutual information maximization, have been particularly successful in this task but still struggle in the context of robotic manipulation. As it requires impacting a possibly large set of degrees of freedom composing the environment, mutual information maximization fails alone in producing useful manipulation behaviors. To address this limitation, we introduce SLIM, a multi-critic learning approach for skill discovery with a particular focus on robotic manipulation. Our main insight is that utilizing multiple critics in an actor-critic framework to gracefully combine multiple reward functions leads to a significant improvement in latent-variable skill discovery for robotic manipulation while overcoming possible interference occurring among rewards which hinders convergence to useful skills. Furthermore, in the context of tabletop manipulation, we demonstrate the applicability of our novel skill discovery approach to acquire safe and efficient motor primitives in a hierarchical reinforcement learning fashion and leverage them through planning, surpassing the state-of-the-art approaches for skill discovery by a large margin.
Shielding is a popular technique for achieving safe reinforcement learning (RL). However, classical shielding approaches come with quite restrictive assumptions making them difficult to deploy in complex environments, particularly those with continuous state or action spaces. In this paper we extend the more versatile approximate model-based shielding (AMBS) framework to the continuous setting. In particular we use Safety Gym as our test-bed, allowing for a more direct comparison of AMBS with popular constrained RL algorithms. We also provide strong probabilistic safety guarantees for the continuous setting. In addition, we propose two novel penalty techniques that directly modify the policy gradient, which empirically provide more stable convergence in our experiments.
Numerous examples in the literature proved that deep learning models have the ability to work well with multimodal data. Recently, CLIP has enabled deep learning systems to learn shared latent spaces between images and text descriptions, with outstanding zero- or few-shot results in downstream tasks. In this paper we explore the same idea proposed by CLIP but applied to the speech domain, where the phonetic and acoustic spaces usually coexist. We train a CLIP-based model with the aim to learn shared representations of phonetic and acoustic spaces. The results show that the proposed model is sensible to phonetic changes, with a 91% of score drops when replacing 20% of the phonemes at random, while providing substantial robustness against different kinds of noise, with a 10% performance drop when mixing the audio with 75% of Gaussian noise. We also provide empirical evidence showing that the resulting embeddings are useful for a variety of downstream applications, such as intelligibility evaluation and the ability to leverage rich pre-trained phonetic embeddings in speech generation task. Finally, we discuss potential applications with interesting implications for the speech generation and recognition fields.
Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability assumption, which has recently evolved into the concept of coseparability. This advancement offers a more efficient core representation for the original data. However, in the real world, the data is more natural to be represented as a multi-dimensional array, such as images or videos. The NMF's application to high-dimensional data involves vectorization, which risks losing essential multi-dimensional correlations. To retain these inherent correlations in the data, we turn to tensors (multidimensional arrays) and leverage the tensor t-product. This approach extends the coseparable NMF to the tensor setting, creating what we term coseparable Nonnegative Tensor Factorization (NTF). In this work, we provide an alternating index selection method to select the coseparable core. Furthermore, we validate the t-CUR sampling theory and integrate it with the tensor Discrete Empirical Interpolation Method (t-DEIM) to introduce an alternative, randomized index selection process. These methods have been tested on both synthetic and facial analysis datasets. The results demonstrate the efficiency of coseparable NTF when compared to coseparable NMF.
This study investigates self-supervised learning techniques to obtain representations of Event Sequences. It is a key modality in various applications, including but not limited to banking, e-commerce, and healthcare. We perform a comprehensive study of generative and contrastive approaches in self-supervised learning, applying them both independently. We find that there is no single supreme method. Consequently, we explore the potential benefits of combining these approaches. To achieve this goal, we introduce a novel method that aligns generative and contrastive embeddings as distinct modalities, drawing inspiration from contemporary multimodal research. Generative and contrastive approaches are often treated as mutually exclusive, leaving a gap for their combined exploration. Our results demonstrate that this aligned model performs at least on par with, and mostly surpasses, existing methods and is more universal across a variety of tasks. Furthermore, we demonstrate that self-supervised methods consistently outperform the supervised approach on our datasets.
As an effective strategy, data augmentation (DA) alleviates data scarcity scenarios where deep learning techniques may fail. It is widely applied in computer vision then introduced to natural language processing and achieves improvements in many tasks. One of the main focuses of the DA methods is to improve the diversity of training data, thereby helping the model to better generalize to unseen testing data. In this survey, we frame DA methods into three categories based on the diversity of augmented data, including paraphrasing, noising, and sampling. Our paper sets out to analyze DA methods in detail according to the above categories. Further, we also introduce their applications in NLP tasks as well as the challenges.
Generalization to out-of-distribution (OOD) data is a capability natural to humans yet challenging for machines to reproduce. This is because most learning algorithms strongly rely on the i.i.d.~assumption on source/target data, which is often violated in practice due to domain shift. Domain generalization (DG) aims to achieve OOD generalization by using only source data for model learning. Since first introduced in 2011, research in DG has made great progresses. In particular, intensive research in this topic has led to a broad spectrum of methodologies, e.g., those based on domain alignment, meta-learning, data augmentation, or ensemble learning, just to name a few; and has covered various vision applications such as object recognition, segmentation, action recognition, and person re-identification. In this paper, for the first time a comprehensive literature review is provided to summarize the developments in DG for computer vision over the past decade. Specifically, we first cover the background by formally defining DG and relating it to other research fields like domain adaptation and transfer learning. Second, we conduct a thorough review into existing methods and present a categorization based on their methodologies and motivations. Finally, we conclude this survey with insights and discussions on future research directions.
Deep Learning has implemented a wide range of applications and has become increasingly popular in recent years. The goal of multimodal deep learning is to create models that can process and link information using various modalities. Despite the extensive development made for unimodal learning, it still cannot cover all the aspects of human learning. Multimodal learning helps to understand and analyze better when various senses are engaged in the processing of information. This paper focuses on multiple types of modalities, i.e., image, video, text, audio, body gestures, facial expressions, and physiological signals. Detailed analysis of past and current baseline approaches and an in-depth study of recent advancements in multimodal deep learning applications has been provided. A fine-grained taxonomy of various multimodal deep learning applications is proposed, elaborating on different applications in more depth. Architectures and datasets used in these applications are also discussed, along with their evaluation metrics. Last, main issues are highlighted separately for each domain along with their possible future research directions.
Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.