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Detection of out-of-distribution samples is one of the critical tasks for real-world applications of computer vision. The advancement of deep learning has enabled us to analyze real-world data which contain unexplained samples, accentuating the need to detect out-of-distribution instances more than before. GAN-based approaches have been widely used to address this problem due to their ability to perform distribution fitting; however, they are accompanied by training instability and mode collapse. We propose a simple yet efficient reconstruction-based method that avoids adding complexities to compensate for the limitations of GAN models while outperforming them. Unlike previous reconstruction-based works that only utilize reconstruction error or generated samples, our proposed method simultaneously incorporates both of them in the detection task. Our model, which we call "Connective Novelty Detection" has two subnetworks, an autoencoder, and a binary classifier. The autoencoder learns the representation of the positive class by reconstructing them. Then, the model creates negative and connected positive examples using real and generated samples. Negative instances are generated via manipulating the real data, so their distribution is close to the positive class to achieve a more accurate boundary for the classifier. To boost the robustness of the detection to reconstruction error, connected positive samples are created by combining the real and generated samples. Finally, the binary classifier is trained using connected positive and negative examples. We demonstrate a considerable improvement in novelty detection over state-of-the-art methods on MNIST and Caltech-256 datasets.

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important challenges: Existing guarantees (1) typically only hold for the averaged iterates rather than the more desirable last iterates, (2) lack convergence metrics that capture the scales of the variables such as Wasserstein distances, and (3) mainly apply to elementary schemes such as stochastic gradient Langevin dynamics. In this paper, we develop a new framework that lifts the above issues by harnessing several tools from the theory of dynamical systems. Our key result is that, for a large class of state-of-the-art sampling schemes, their last-iterate convergence in Wasserstein distances can be reduced to the study of their continuous-time counterparts, which is much better understood. Coupled with standard assumptions of MCMC sampling, our theory immediately yields the last-iterate Wasserstein convergence of many advanced sampling schemes such as proximal, randomized mid-point, and Runge-Kutta integrators. Beyond existing methods, our framework also motivates more efficient schemes that enjoy the same rigorous guarantees.

Data-driven approaches recently achieved remarkable success in medical image reconstruction, but integration into clinical routine remains challenging due to a lack of generalizability and interpretability. Existing approaches usually require high-quality data-image pairs for training, but such data is not easily available for any imaging protocol and the reconstruction quality can quickly degrade even if only minor changes are made to the protocol. In addition, data-driven methods may create artificial features that can influence the clinicians decision-making. This is unacceptable if the clinician is unaware of the uncertainty associated with the reconstruction. In this paper, we address these challenges in a unified framework based on generative image priors. We propose a novel deep neural network based regularizer which is trained in an unsupervised setting on reference images without requiring any data-image pairs. After training, the regularizer can be used as part of a classical variational approach in combination with any acquisition protocols and shows stable behavior even if the test data deviates significantly from the training data. Furthermore, our probabilistic interpretation provides a distribution of reconstructions and hence allows uncertainty quantification. We demonstrate our approach on parallel magnetic resonance imaging, where results show competitive performance with SotA end-to-end deep learning methods, while preserving the flexibility of the acquisition protocol and allowing for uncertainty quantification.

We study a variant of classical clustering formulations in the context of algorithmic fairness, known as diversity-aware clustering. In this variant we are given a collection of facility subsets, and a solution must contain at least a specified number of facilities from each subset while simultaneously minimizing the clustering objective ($k$-median or $k$-means). We investigate the fixed-parameter tractability of these problems and show several negative hardness and inapproximability results, even when we afford exponential running time with respect to some parameters. Motivated by these results we identify natural parameters of the problem, and present fixed-parameter approximation algorithms with approximation ratios $\big(1 + \frac{2}{e} +\epsilon \big)$ and $\big(1 + \frac{8}{e}+ \epsilon \big)$ for diversity-aware $k$-median and diversity-aware $k$-means respectively, and argue that these ratios are essentially tight assuming the gap-exponential time hypothesis. We also present a simple and more practical bicriteria approximation algorithm with better running time bounds. We finally propose efficient and practical heuristics. We evaluate the scalability and effectiveness of our methods in a wide variety of rigorously conducted experiments, on both real and synthetic data.

We propose and analyze exact and inexact regularized Newton-type methods for finding a global saddle point of a \textit{convex-concave} unconstrained min-max optimization problem. Compared to their first-order counterparts, investigations of second-order methods for min-max optimization are relatively limited, as obtaining global rates of convergence with second-order information is much more involved. In this paper, we highlight how second-order information can be used to speed up the dynamics of dual extrapolation methods {despite inexactness}. Specifically, we show that the proposed algorithms generate iterates that remain within a bounded set and the averaged iterates converge to an $\epsilon$-saddle point within $O(\epsilon^{-2/3})$ iterations in terms of a gap function. Our algorithms match the theoretically established lower bound in this context and our analysis provides a simple and intuitive convergence analysis for second-order methods without requiring any compactness assumptions. Finally, we present a series of numerical experiments on synthetic and real data that demonstrate the efficiency of the proposed algorithms.

Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is $n^{-1/2}$ for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for ill posed inverse problems.

Feature selection plays a vital role in promoting the classifier's performance. However, current methods ineffectively distinguish the complex interaction in the selected features. To further remove these hidden negative interactions, we propose a GA-like dynamic probability (GADP) method with mutual information which has a two-layer structure. The first layer applies the mutual information method to obtain a primary feature subset. The GA-like dynamic probability algorithm, as the second layer, mines more supportive features based on the former candidate features. Essentially, the GA-like method is one of the population-based algorithms so its work mechanism is similar to the GA. Different from the popular works which frequently focus on improving GA's operators for enhancing the search ability and lowering the converge time, we boldly abandon GA's operators and employ the dynamic probability that relies on the performance of each chromosome to determine feature selection in the new generation. The dynamic probability mechanism significantly reduces the parameter number in GA that making it easy to use. As each gene's probability is independent, the chromosome variety in GADP is more notable than in traditional GA, which ensures GADP has a wider search space and selects relevant features more effectively and accurately. To verify our method's superiority, we evaluate our method under multiple conditions on 15 datasets. The results demonstrate the outperformance of the proposed method. Generally, it has the best accuracy. Further, we also compare the proposed model to the popular heuristic methods like POS, FPA, and WOA. Our model still owns advantages over them.

In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks with state-of-the-art performance. The data is generally represented in the Euclidean space in these domains. Various other domains conform to non-Euclidean space, for which graph is an ideal representation. Graphs are suitable for representing the dependencies and interrelationships between various entities. Traditionally, handcrafted features for graphs are incapable of providing the necessary inference for various tasks from this complex data representation. Recently, there is an emergence of employing various advances in deep learning to graph data-based tasks. This article provides a comprehensive survey of graph neural networks (GNNs) in each learning setting: supervised, unsupervised, semi-supervised, and self-supervised learning. Taxonomy of each graph based learning setting is provided with logical divisions of methods falling in the given learning setting. The approaches for each learning task are analyzed from both theoretical as well as empirical standpoints. Further, we provide general architecture guidelines for building GNNs. Various applications and benchmark datasets are also provided, along with open challenges still plaguing the general applicability of GNNs.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.