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In this paper, we introduce a probabilistic model for learning interpolative decomposition (ID), which is commonly used for feature selection, low-rank approximation, and identifying hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Prior densities with support on the specified subspace are used to address the constraint for the magnitude of the factored component of the observed matrix. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on a variety of real-world datasets including CCLE EC50, CCLE IC50, CTRP EC50,and MovieLens 100K datasets with different sizes, and dimensions, and show that the proposed Bayesian ID GBT and GBTN models lead to smaller reconstructive errors compared to existing randomized approaches., Comment: arXiv admin note: text overlap with arXiv:2205.11025

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimensions and show that the proposed Bayesian NMF GRRN model leads to better predictions and avoids overfitting compared to existing Bayesian NMF approaches.

We revisit the $D_s^-D^{*0}$/$D_s^{*-}D^0$ interaction and the $Z_{cs}(3985)$ state in chiral effective field theory(EFT) up to the next-to-leading order. We examine the relative importance of the leading-order contact, one-eta exchange, next-to-leading-order contact, and two-kaon-exchange contributions. We show that the leading-order and next-to-leading-order contact contributions play the most important role such that the $Z_{cs}(3985)$ state qualifies as a $D_s^-D^{*0}$/$D_s^{*-}D^0$ resonance. On the other hand, the weak one-eta-exchange and weakly energy-dependent two-kaon-exchange contributions are less important in dynamically generating the $Z_{cs}(3985)$ state, indicating that chiral EFT is less predictive in the present situation. Furthermore, we apply the Bayesian method to estimate chiral truncation uncertainties and find that they are of similar magnitude as their statistical counterparts. Our study shows that if $Z_c(3900)$ exists, then SU(3)-flavor symmetry also predicts $Z_{cs}(3985)$ with a certain robustness, i.e., both can be accommodated in the chiral EFT with dominant contact contributions., Comment: 8 pages,5 figures

The goal of this paper is to debunk and dispel the magic behind black-box optimizers and stochastic optimizers. It aims to build a solid foundation on how and why the techniques work. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind the strategies. This tutorial doesn't shy away from addressing both the formal and informal aspects of gradient descent and stochastic optimization methods. By doing so, it hopes to provide readers with a deeper understanding of these techniques as well as the when, the how and the why of applying these algorithms. Gradient descent is one of the most popular algorithms to perform optimization and by far the most common way to optimize machine learning tasks. Its stochastic version receives attention in recent years, and this is particularly true for optimizing deep neural networks. In deep neural networks, the gradient followed by a single sample or a batch of samples is employed to save computational resources and escape from saddle points. In 1951, Robbins and Monro published \textit{A stochastic approximation method}, one of the first modern treatments on stochastic optimization that estimates local gradients with a new batch of samples. And now, stochastic optimization has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this article is to give a self-contained introduction to concepts and mathematical tools in gradient descent and stochastic optimization.

It is well known that we need to choose the hyper-parameters in Momentum, AdaGrad, AdaDelta, and other alternative stochastic optimizers. While in many cases, the hyper-parameters are tuned tediously based on experience becoming more of an art than science. We present a novel per-dimension learning rate method for gradient descent called AdaSmooth. The method is insensitive to hyper-parameters thus it requires no manual tuning of the hyper-parameters like Momentum, AdaGrad, and AdaDelta methods. We show promising results compared to other methods on different convolutional neural networks, multi-layer perceptron, and alternative machine learning tasks. Empirical results demonstrate that AdaSmooth works well in practice and compares favorably to other stochastic optimization methods in neural networks.

We report on the construction of an accurate relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading (NNLO) order. We compare the so-obtained neutron-proton phaseshifts with the next-to-next-to-next-to-leading order (N$^3$LO) nonrelativistic ones and we show that up to $T_\mathrm{lab.}=200$ MeV, the relativistic chiral nuclear force can describe the PWA93 phaseshifts and inelasticities as well as its N$^3$LO nonrelativistic counterparts. As a result, the relativistic chiral nuclear force can be readily used for relativistic ab initio nuclear structure, reaction, as well astrophysical studies., Comment: 10 pages, 2 figures; Contribution to the 10th International Workshop on Chiral Dynamics

SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good performance in terms of various performance measurements, trading opportunities, peak or trough behaviors in the time series are all hampered by underestimating or overestimating the volatility. We propose a blending ARCH (BARCH) and an augmented BARCH (aBARCH) model to overcome this kind of problem and make the prediction towards better peak or trough behaviors. The method is illustrated using real data sets including SH300 and S&P500. The empirical results obtained suggest that the augmented and blending models improve the volatility forecasting ability.