Tensor data are multi-dimension arrays. Low-rank decomposition-based regression methods with tensor predictors exploit the structural information in tensor predictors while significantly reducing the number of parameters in tensor regression. We propose a method named NA$_0$CT$^2$ (Noise Augmentation for $\ell_0$ regularization on Core Tensor in Tucker decomposition) to regularize the parameters in tensor regression (TR), coupled with Tucker decomposition. We establish theoretically that NA$_0$CT$^2$ achieves exact $\ell_0$ regularization in linear TR and generalized linear TR on the core tensor from the Tucker decomposition. To our knowledge, NA$_0$CT$^2$ is the first Tucker decomposition-based regularization method in TR to achieve $\ell_0$ in core tensor. NA$_0$CT$^2$ is implemented through an iterative procedure and involves two simple steps in each iteration -- generating noisy data based on the core tensor from the Tucker decomposition of the updated parameter estimate and running a regular GLM on noise-augmented data on vectorized predictors. We demonstrate the implementation of NA$_0$CT$^2$ and its $\ell_0$ regularization effect in both simulation studies and real data applications. The results suggest that NA$_0$CT$^2$ improves predictions compared to other decomposition-based TR approaches, with or without regularization and it also helps to identify important predictors though not designed for that purpose.

Pre-trained language models have led to a new state-of-the-art in many NLP tasks. However, for topic modeling, statistical generative models such as LDA are still prevalent, which do not easily allow incorporating contextual word vectors. They might yield topics that do not align very well with human judgment. In this work, we propose a novel topic modeling and inference algorithm. We suggest a bag of sentences (BoS) approach using sentences as the unit of analysis. We leverage pre-trained sentence embeddings by combining generative process models with clustering. We derive a fast inference algorithm based on expectation maximization, hard assignments, and an annealing process. Our evaluation shows that our method yields state-of-the art results with relatively little computational demands. Our methods is more flexible compared to prior works leveraging word embeddings, since it provides the possibility to customize topic-document distributions using priors. Code is at \url{https://github.com/JohnTailor/BertSenClu}.

Stochastic gradient descent is a workhorse for training deep neural networks due to its excellent generalization performance. Several studies demonstrated this success is attributed to the implicit bias of the method that prefers a flat minimum and developed new methods based on this perspective. Recently, Izmailov et al. (2018) empirically observed that an averaged stochastic gradient descent with a large step size can bring out the implicit bias more effectively and can converge more stably to a flat minimum than the vanilla stochastic gradient descent. In our work, we theoretically justify this observation by showing that the averaging scheme improves the bias-optimization tradeoff coming from the stochastic gradient noise: a large step size amplifies the bias but makes convergence unstable, and vice versa. Specifically, we show that the averaged stochastic gradient descent can get closer to a solution of a penalized objective on the sharpness than the vanilla stochastic gradient descent using the same step size under certain conditions. In experiments, we verify our theory and show this learning scheme significantly improves performance.

Neural Additive Models (NAMs) (Agarwal et al., and have become the go-to method for problems 2021b) were recently proposed as a class of Neural Networks, requiring high-level predictive power. There has that impose an additivity constraint on the input data been extensive research on how DNNs arrive at and thus allow to directly derive the feature-wise contribution their decisions, however, the inherently uninterpretable onto the generated predictions as a function of the input networks remain up to this day mostly domain. While this indeed yields an exact representation of unobservable "black boxes". In recent years, the the decision making process, NAMs are nevertheless highly field has seen a push towards interpretable neural complex functions that are characterized by hundreds of networks, such as the visually interpretable thousands of parameters and thus fail to address additional Neural Additive Models (NAMs). We propose dimensions of interpretability (Murdoch et al., 2019). To a further step into the direction of intelligibility this end, we propose the use of Structural Neural Additive beyond the mere visualization of feature effects Models (SNAMs) as a way to achieve the same (and and propose Structural Neural Additive Models even better) predictive performance with a fraction of the (SNAMs). A modeling framework that combines parameters required, while providing intelligibility beyond classical and clearly interpretable statistical methods mere visualizations. The contributions of SNAMs can be with the predictive power of neural applications.

Statistical power is a measure of the replicability of a categorical hypothesis test. Formally, it is the probability of detecting an effect, if there is a true effect present in the population. Hence, optimizing statistical power as a function of some parameters of a hypothesis test is desirable. However, for most hypothesis tests, the explicit functional form of statistical power for individual model parameters is unknown; but calculating power for a given set of values of those parameters is possible using simulated experiments. These simulated experiments are usually computationally expensive. Hence, developing the entire statistical power manifold using simulations can be very time-consuming. We propose a novel genetic algorithm-based framework for learning statistical power manifolds. For a multiple linear regression $F$-test, we show that the proposed algorithm/framework learns the statistical power manifold much faster as compared to a brute-force approach as the number of queries to the power oracle is significantly reduced. We also show that the quality of learning the manifold improves as the number of iterations increases for the genetic algorithm. Such tools are useful for evaluating statistical power trade-offs when researchers have little information regarding a priori best guesses of primary effect sizes of interest or how sampling variability in non-primary effects impacts power for primary ones.

Despite being highly over-parametrized, and having the ability to fully interpolate the training data, deep networks are known to generalize well to unseen data. It is now understood that part of the reason for this is that the training algorithms used have certain implicit regularization properties that ensure interpolating solutions with "good" properties are found. This is best understood in linear over-parametrized models where it has been shown that the celebrated stochastic gradient descent (SGD) algorithm finds an interpolating solution that is closest in Euclidean distance to the initial weight vector. Different regularizers, replacing Euclidean distance with Bregman divergence, can be obtained if we replace SGD with stochastic mirror descent (SMD). Empirical observations have shown that in the deep network setting, SMD achieves a generalization performance that is different from that of SGD (and which depends on the choice of SMD's potential function. In an attempt to begin to understand this behavior, we obtain the generalization error of SMD for over-parametrized linear models for a binary classification problem where the two classes are drawn from a Gaussian mixture model. We present simulation results that validate the theory and, in particular, introduce two data models, one for which SMD with an $\ell_2$ regularizer (i.e., SGD) outperforms SMD with an $\ell_1$ regularizer, and one for which the reverse happens.

The growing use of automated decision-making in critical applications, such as crime prediction and college admission, has raised questions about fairness in machine learning. How can we decide whether different treatments are reasonable or discriminatory? In this paper, we investigate discrimination in machine learning from a visual analytics perspective and propose an interactive visualization tool, DiscriLens, to support a more comprehensive analysis. To reveal detailed information on algorithmic discrimination, DiscriLens identifies a collection of potentially discriminatory itemsets based on causal modeling and classification rules mining. By combining an extended Euler diagram with a matrix-based visualization, we develop a novel set visualization to facilitate the exploration and interpretation of discriminatory itemsets. A user study shows that users can interpret the visually encoded information in DiscriLens quickly and accurately. Use cases demonstrate that DiscriLens provides informative guidance in understanding and reducing algorithmic discrimination.

When modeling related tasks in computer vision, Multi-Task Learning (MTL) can outperform Single-Task Learning (STL) due to its ability to capture intrinsic relatedness among tasks. However, MTL may encounter the insufficient training problem, i.e., some tasks in MTL may encounter non-optimal situation compared with STL. A series of studies point out that too much gradient noise would lead to performance degradation in STL, however, in the MTL scenario, Inter-Task Gradient Noise (ITGN) is an additional source of gradient noise for each task, which can also affect the optimization process. In this paper, we point out ITGN as a key factor leading to the insufficient training problem. We define the Gradient-to-Noise Ratio (GNR) to measure the relative magnitude of gradient noise and design the MaxGNR algorithm to alleviate the ITGN interference of each task by maximizing the GNR of each task. We carefully evaluate our MaxGNR algorithm on two standard image MTL datasets: NYUv2 and Cityscapes. The results show that our algorithm outperforms the baselines under identical experimental conditions.

In recent years, graph representation learning has achieved remarkable success while suffering from low-quality data problems. As a mature technology to improve data quality in computer vision, data augmentation has also attracted increasing attention in graph domain. For promoting the development of this emerging research direction, in this survey, we comprehensively review and summarize the existing graph data augmentation (GDAug) techniques. Specifically, we first summarize a variety of feasible taxonomies, and then classify existing GDAug studies based on fine-grained graph elements. Furthermore, for each type of GDAug technique, we formalize the general definition, discuss the technical details, and give schematic illustration. In addition, we also summarize common performance metrics and specific design metrics for constructing a GDAug evaluation system. Finally, we summarize the applications of GDAug from both data and model levels, as well as future directions. Latest advances in GDAug are summarized in a GitHub repository: https://github.com/jjzhou012/GDAug-Survey.

Multimodal named entity recognition (MNER) and multimodal relation extraction (MRE) are two fundamental subtasks in the multimodal knowledge graph construction task. However, the existing methods usually handle two tasks independently, which ignores the bidirectional interaction between them. This paper is the first to propose jointly performing MNER and MRE as a joint multimodal entity-relation extraction task (JMERE). Besides, the current MNER and MRE models only consider aligning the visual objects with textual entities in visual and textual graphs but ignore the entity-entity relationships and object-object relationships. To address the above challenges, we propose an edge-enhanced graph alignment network and a word-pair relation tagging (EEGA) for JMERE task. Specifically, we first design a word-pair relation tagging to exploit the bidirectional interaction between MNER and MRE and avoid the error propagation. Then, we propose an edge-enhanced graph alignment network to enhance the JMERE task by aligning nodes and edges in the cross-graph. Compared with previous methods, the proposed method can leverage the edge information to auxiliary alignment between objects and entities and find the correlations between entity-entity relationships and object-object relationships. Experiments are conducted to show the effectiveness of our model.