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The task of precisely learning the probability distribution of rows within tabular data and producing authentic synthetic samples is both crucial and non-trivial. Wasserstein generative adversarial network (WGAN) marks a notable improvement in generative modeling, addressing the challenges faced by its predecessor, generative adversarial network. However, due to the mixed data types and multimodalities prevalent in tabular data, the delicate equilibrium between the generator and discriminator, as well as the inherent instability of Wasserstein distance in high dimensions, WGAN often fails to produce high-fidelity samples. To this end, we propose POTNet (Penalized Optimal Transport Network), a generative deep neural network based on a novel, robust, and interpretable marginally-penalized Wasserstein (MPW) loss. POTNet can effectively model tabular data containing both categorical and continuous features. Moreover, it offers the flexibility to condition on a subset of features. We provide theoretical justifications for the motivation behind the MPW loss. We also empirically demonstrate the effectiveness of our proposed method on four different benchmarks across a variety of real-world and simulated datasets. Our proposed model achieves orders of magnitude speedup during the sampling stage compared to state-of-the-art generative models for tabular data, thereby enabling efficient large-scale synthetic data generation.

Gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges of optimization problems arising in data science. Focusing on data science applications with expensive objective function evaluations yet inexpensive gradient function evaluations, gradient methods that never make objective function evaluations are either being rejuvenated or actively developed. However, as we show, such gradient methods are all susceptible to catastrophic divergence under realistic conditions for data science applications. In light of this, gradient methods which make use of objective function evaluations become more appealing, yet, as we show, can result in an exponential increase in objective evaluations between accepted iterates. As a result, existing gradient methods are poorly suited to the needs of optimization problems arising from data science. In this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent catastrophic divergence and avoid an explosion in objective evaluations between accepted iterates. Our methodology allows for specific procedures that can make use of specific step size selection methodologies or search direction strategies, and we develop a novel step size selection methodology that is well-suited to data science applications. We show that a procedure resulting from our methodology is highly competitive with standard optimization methods on CUTEst test problems. We then show a procedure resulting from our methodology is highly favorable relative to standard optimization methods on optimization problems arising in our target data science applications. Thus, we provide a novel gradient methodology that is better suited to optimization problems arising in data science.

The Quantum Alternating Operator Ansatz (QAOA) is a prominent variational quantum algorithm for solving combinatorial optimization problems. Its effectiveness depends on identifying input parameters that yield high-quality solutions. However, understanding the complexity of training QAOA remains an under-explored area. Previous results have given analytical performance guarantees for a small, fixed number of parameters. At the opposite end of the spectrum, barren plateaus are likely to emerge at $\Omega(n)$ parameters for $n$ qubits. In this work, we study the difficulty of training in the intermediate regime, which is the focus of most current numerical studies and near-term hardware implementations. Through extensive numerical analysis of the quality and quantity of local minima, we argue that QAOA landscapes can exhibit a superpolynomial growth in the number of low-quality local minima even when the number of parameters scales logarithmically with $n$. This means that the common technique of gradient descent from randomly initialized parameters is doomed to fail beyond small $n$, and emphasizes the need for good initial guesses of the optimal parameters.

We develop a statistical inference method for an optimal transport map between distributions on real numbers with uniform confidence bands. The concept of optimal transport (OT) is used to measure distances between distributions, and OT maps are used to construct the distance. OT has been applied in many fields in recent years, and its statistical properties have attracted much interest. In particular, since the OT map is a function, a uniform norm-based statistical inference is significant for visualization and interpretation. In this study, we derive a limit distribution of a uniform norm of an estimation error for the OT map, and then develop a uniform confidence band based on it. In addition to our limit theorem, we develop a bootstrap method with kernel smoothing, then also derive its validation and guarantee on an asymptotic coverage probability of the confidence band. Our proof is based on the functional delta method and the representation of OT maps on the reals.

We propose Structured Language Generation Model (SLGM), a mixture of new loss function and inference method for better generalization of structured outputs. Previous studies on structure prediction (e.g. NER, RE) make use of explicit dataset information, which would boost performance, yet it might pose challenges to robust generalization in real-world situations. Instead, our model gives generalized format information about data indirectly. With format information, we could reduce sequence-to-sequence problem into classification problem via loss calibration and formatted decoding. Our experimental results showed SLGM successfully maintain performance without dataset information, and showed much less format errors. We also showed our model can work like adapters on individual dataset, with no additional training.

We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence, and uniqueness statements of the corresponding variational methods. We also obtain optimal error estimates of the semidiscrete scheme in corresponding B\^ochner spaces. Finally, we construct a fully discrete scheme through a backward Euler discretization of the time derivative, and prove well-posedness statements for this fully discrete scheme. Our findings show that the mixed approach removes some theoretical impediments to analysis and is numerically easier to implement. We provide numerical simulations for the mixed formulation approach using $C^0$ Taylor-Hood finite elements on several domains. Our numerical results confirm that the algorithm has optimal convergence in accordance with the observed theoretical results.

Extremely large-scale massive multiple-input multiple-output (XL-MIMO) systems introduce the much higher channel dimensionality and incur the additional near-field propagation effect, aggravating the computation load and the difficulty to acquire the prior knowledge for channel estimation. In this article, an XL-MIMO channel network (XLCNet) is developed to estimate the high-dimensional channel, which is a universal solution for both the near-field users and far-field users with different channel statistics. Furthermore, a compressed XLCNet (C-XLCNet) is designed via weight pruning and quantization to accelerate the model inference as well as to facilitate the model storage and transmission. Simulation results show the performance superiority and universality of XLCNet. Compared to XLCNet, C-XLCNet incurs the limited performance loss while reducing the computational complexity and model size by about $10 \times$ and $36 \times$, respectively.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Cold-start problems are long-standing challenges for practical recommendations. Most existing recommendation algorithms rely on extensive observed data and are brittle to recommendation scenarios with few interactions. This paper addresses such problems using few-shot learning and meta learning. Our approach is based on the insight that having a good generalization from a few examples relies on both a generic model initialization and an effective strategy for adapting this model to newly arising tasks. To accomplish this, we combine the scenario-specific learning with a model-agnostic sequential meta-learning and unify them into an integrated end-to-end framework, namely Scenario-specific Sequential Meta learner (or s^2 meta). By doing so, our meta-learner produces a generic initial model through aggregating contextual information from a variety of prediction tasks while effectively adapting to specific tasks by leveraging learning-to-learn knowledge. Extensive experiments on various real-world datasets demonstrate that our proposed model can achieve significant gains over the state-of-the-arts for cold-start problems in online recommendation. Deployment is at the Guess You Like session, the front page of the Mobile Taobao.

We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.