In many scientific research and engineering applications, where repeated simulations of complex systems are conducted, a surrogate is commonly adopted to quickly estimate the whole system. To reduce the expensive cost of generating training examples, it has become a promising approach to combine the results of low-fidelity (fast but inaccurate) and high-fidelity (slow but accurate) simulations. Despite the fast developments of multi-fidelity fusion techniques, most existing methods require particular data structures and do not scale well to high-dimensional output. To resolve these issues, we generalize the classic autoregression (AR), which is wildly used due to its simplicity, robustness, accuracy, and tractability, and propose generalized autoregression (GAR) using tensor formulation and latent features. GAR can deal with arbitrary dimensional outputs and arbitrary multifidelity data structure to satisfy the demand of multi-fidelity fusion for complex problems; it admits a fully tractable likelihood and posterior requiring no approximate inference and scales well to high-dimensional problems.

Self-supervision provides effective representations for downstream tasks without requiring labels. However, existing approaches lag behind fully supervised training and are often not thought beneficial beyond obviating or reducing the need for annotations. We find that self-supervision can benefit robustness in a variety of ways, including robustness to adversarial examples, label corruption, and common input corruptions. Additionally, self-supervision greatly benefits out-of-distribution detection on difficult, near-distribution outliers, so much so that it exceeds the performance of fully supervised methods. These results demonstrate the promise of self-supervision for improving robustness and uncertainty estimation and establish these tasks as new axes of evaluation for future self-supervised learning research.

Self- and semi-supervised learning frameworks have made significant progress in training machine learning models with limited labeled data in image and language domains. These methods heavily rely on the unique structure in the domain datasets (such as spatial relationships in images or semantic relationships in language). They are not adaptable to general tabular data which does not have the same explicit structure as image and language data. In this paper, we fill this gap by proposing novel self- and semi-supervised learning frameworks for tabular data, which we refer to collectively as VIME (Value Imputation and Mask Estimation). We create a novel pretext task of estimating mask vectors from corrupted tabular data in addition to the reconstruction pretext task for self-supervised learning.

Partial-label learning (PLL) is a multi-class classification problem, where each training example is associated with a set of candidate labels. Even though many practical PLL methods have been proposed in the last two decades, there lacks a theoretical understanding of the consistency of those methods - none of the PLL methods hitherto possesses a generation process of candidate label sets, and then it is still unclear why such a method works on a specific dataset and when it may fail given a different dataset. In this paper, we propose the first generation model of candidate label sets, and develop two PLL methods that are guaranteed to be provably consistent, i.e., one is risk-consistent and the other is classifier-consistent. Our methods are advantageous, since they are compatible with any deep network or stochastic optimizer. Furthermore, thanks to the generation model, we would be able to answer the two questions above by testing if the generation model matches given candidate label sets.

We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that includes the arithmetic, geometric and harmonic means as particular cases. We analyze it in expectation under a Multilayer Stochastic Block Model and verify numerically that it outperforms state of the art methods. Moreover, we introduce a matrix-free numerical scheme based on contour integral quadratures and Krylov subspace solvers that scales to large sparse multilayer graphs.

Unsupervised semantic segmentation is a challenging task that segments images into semantic groups without manual annotation. Prior works have primarily focused on leveraging prior knowledge of semantic consistency or priori concepts from self-supervised learning methods, which often overlook the coherence property of image segments. In this paper, we demonstrate that the smoothness prior, asserting that close features in a metric space share the same semantics, can significantly simplify segmentation by casting unsupervised semantic segmentation as an energy minimization problem. Under this paradigm, we propose a novel approach called SmooSeg that harnesses self-supervised learning methods to model the closeness relationships among observations as smoothness signals. To effectively discover coherent semantic segments, we introduce a novel smoothness loss that promotes piecewise smoothness within segments while preserving discontinuities across different segments.

Within months of birth, children develop meaningful expectations about the world around them. How much of this early knowledge can be explained through generic learning mechanisms applied to sensory data, and how much of it requires more substantive innate inductive biases? Addressing this fundamental question in its full generality is currently infeasible, but we can hope to make real progress in more narrowly defined domains, such as the development of high-level visual categories, thanks to improvements in data collecting technology and recent progress in deep learning. In this paper, our goal is precisely to achieve such progress by utilizing modern self-supervised deep learning methods and a recent longitudinal, egocentric video dataset recorded from the perspective of three young children (Sullivan et al., 2020). Our results demonstrate the emergence of powerful, high-level visual representations from developmentally realistic natural videos using generic self-supervised learning objectives.

Few-shot classification aims to learn a classifier to recognize unseen classes during training, where the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples. A recent solution to this problem is calibrating the distribution of these few sample classes by transferring statistics from the base classes with sufficient examples, where how to decide the transfer weights from base classes to novel classes is the key. However, principled approaches for learning the transfer weights have not been carefully studied. To this end, we propose a novel distribution calibration method by learning the adaptive weight matrix between novel samples and base classes, which is built upon a hierarchical Optimal Transport (H-OT) framework. By minimizing the high-level OT distance between novel samples and base classes, we can view the learned transport plan as the adaptive weight information for transferring the statistics of base classes. The learning of the cost function between a base class and novel class in the high-level OT leads to the introduction of the low-level OT, which considers the weights of all the data samples in the base class.

Visual and audio modalities are highly correlated, yet they contain different information. Their strong correlation makes it possible to predict the semantics of one from the other with good accuracy. Their intrinsic differences make cross-modal prediction a potentially more rewarding pretext task for self-supervised learning of video and audio representations compared to within-modality learning. Based on this intuition, we propose Cross-Modal Deep Clustering (XDC), a novel self-supervised method that leverages unsupervised clustering in one modality (e.g., audio) as a supervisory signal for the other modality (e.g., video). This cross-modal supervision helps XDC utilize the semantic correlation and the differences between the two modalities.

We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that oracle, our framework automatically generates a corresponding convex and smooth loss function. As we show, adding a projection as output layer provably makes the loss smaller. We identify the marginal polytope, the output space's convex hull, as the best convex set on which to project.