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Considering the shortcomings of the traditional sample covariance matrix estimation, this paper proposes an improved global minimum variance portfolio model and named spectral corrected and regularized global minimum variance portfolio (SCRGMVP), which is better than the traditional risk model. The key of this method is that under the assumption that the population covariance matrix follows the spiked model and the method combines the design idea of the sample spectrally-corrected covariance matrix and regularized. The simulation of real and synthetic data shows that our method is not only better than the performance of traditional sample covariance matrix estimation (SCME), shrinkage estimation (SHRE), weighted shrinkage estimation (WSHRE) and simple spectral correction estimation (SCE), but also has lower computational complexity.

Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We implement efficient stochastic gradient ascent procedures based on the use of control variates or the reparameterization trick and demonstrate that the proposed implementations provide a fast and accurate alternative to Markov chain Monte Carlo sampling. Additionally, we present sequential updating versions of our variational algorithms, which are suitable for efficient portfolio construction and dynamic asset allocation.

This paper underscores the vital role of the chi-square test within political science research utilizing structural equation modeling (SEM). The ongoing debate regarding the inclusion of chi-square test statistics alongside fit indices in result presentations has sparked controversy. Despite the recognized limitations of relying solely on the chi-square test, its judicious application can enhance its effectiveness in evaluating model fit and specification. To exemplify this, we present three common scenarios pertinent to political science research where fit indices may inadequately address goodness-of-fit concerns, while the chi-square statistic can be effectively harnessed. Through Monte Carlo simulations, we examine strategies for enhancing chi-square tests within these scenarios, showcasing the potential of appropriately employed chi-square tests to provide a comprehensive model fit assessment. Our recommendation is to report both the chi-square test and fit indices, with a priority on precise model specification to ensure the trustworthiness of model fit indicators.

With the increasing popularity and accessibility of high dynamic range (HDR) photography, tone mapping operators (TMOs) for dynamic range compression are practically demanding. In this paper, we develop a two-stage neural network-based TMO that is self-calibrated and perceptually optimized. In Stage one, motivated by the physiology of the early stages of the human visual system, we first decompose an HDR image into a normalized Laplacian pyramid. We then use two lightweight deep neural networks (DNNs), taking the normalized representation as input and estimating the Laplacian pyramid of the corresponding LDR image. We optimize the tone mapping network by minimizing the normalized Laplacian pyramid distance (NLPD), a perceptual metric aligning with human judgments of tone-mapped image quality. In Stage two, the input HDR image is self-calibrated to compute the final LDR image. We feed the same HDR image but rescaled with different maximum luminances to the learned tone mapping network, and generate a pseudo-multi-exposure image stack with different detail visibility and color saturation. We then train another lightweight DNN to fuse the LDR image stack into a desired LDR image by maximizing a variant of the structural similarity index for multi-exposure image fusion (MEF-SSIM), which has been proven perceptually relevant to fused image quality. The proposed self-calibration mechanism through MEF enables our TMO to accept uncalibrated HDR images, while being physiology-driven. Extensive experiments show that our method produces images with consistently better visual quality. Additionally, since our method builds upon three lightweight DNNs, it is among the fastest local TMOs.

We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL). When the state space is large or continuous, traditional tabular approaches are unfeasible and some form of function approximation is mandatory. In this paper, we introduce an optimistically-initialized variant of the popular randomized least-squares value iteration (RLSVI), a model-free algorithm where exploration is induced by perturbing the least-squares approximation of the action-value function. Under the assumption that the Markov decision process has low-rank transition dynamics, we prove that the frequentist regret of RLSVI is upper-bounded by $\widetilde O(d^2 H^2 \sqrt{T})$ where $ d $ are the feature dimension, $ H $ is the horizon, and $ T $ is the total number of steps. To the best of our knowledge, this is the first frequentist regret analysis for randomized exploration with function approximation.

We propose a Bayesian meta-analysis to infer the current expansion rate of the Universe, called the Hubble constant ($H_0$), via time delay cosmography. Inputs of the meta-analysis are estimates of two properties for each pair of gravitationally lensed images; time delay and Fermat potential difference estimates with their standard errors. A meta-analysis can be appealing in practice because obtaining each estimate from even a single lens system involves substantial human efforts, and thus estimates are often separately obtained and published. This work focuses on combining these estimates from independent studies to infer $H_0$ in a robust manner. For this purpose, we adopt Student's $t$ error for the inputs of the meta-analysis. We investigate properties of the resulting $H_0$ estimate via two simulation studies with realistic imaging data. It turns out that the meta-analysis can infer $H_0$ with sub-percent bias and about 1 percent level of coefficient of variation, even when 30 percent of inputs are manipulated to be outliers. We also apply the meta-analysis to three gravitationally lensed systems, and estimate $H_0$ by $75.632 \pm 6.918$ (km/second/Mpc), which covers a wide range of $H_0$ estimates obtained under different physical processes. An R package, h0, is publicly available for fitting the proposed meta-analysis.

While most research into speech synthesis has focused on synthesizing high-quality speech for in-dataset speakers, an equally essential yet unsolved problem is synthesizing speech for unseen speakers who are out-of-dataset with limited reference data, i.e., speaker adaptive speech synthesis. Many studies have proposed zero-shot speaker adaptive text-to-speech and voice conversion approaches aimed at this task. However, most current approaches suffer from the degradation of naturalness and speaker similarity when synthesizing speech for unseen speakers (i.e., speakers not in the training dataset) due to the poor generalizability of the model in out-of-distribution data. To address this problem, we propose GZS-TV, a generalizable zero-shot speaker adaptive text-to-speech and voice conversion model. GZS-TV introduces disentangled representation learning for both speaker embedding extraction and timbre transformation to improve model generalization and leverages the representation learning capability of the variational autoencoder to enhance the speaker encoder. Our experiments demonstrate that GZS-TV reduces performance degradation on unseen speakers and outperforms all baseline models in multiple datasets.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.