**Variational Inference for Nonlinear Dynamics (VIND)**

Latent variable models have been widely applied for the analysis and visualization of large datasets. In the case of sequential data, closed-form inference is possible when the transition and observation functions are linear. However, approximate inference techniques are usually necessary when dealing with nonlinear dynamics and observation functions. Here, we propose a novel variational inference framework for the explicit modeling of time series, Variational Inference for Nonlinear Dynamics (VIND), that is able to uncover nonlinear observation and transition functions from sequential data. The framework includes a structured approximate posterior, and an algorithm that relies on the fixed-point iteration method to find the best estimate for latent trajectories. We apply the method to several datasets and show that it is able to accurately infer the underlying dynamics of these systems, in some cases substantially outperforming state-of-the-art methods. … **Simple Stochastic Recursive Gradient Descent (SSRGD)**

We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad unstable saddle points. We show that a simple perturbed version of stochastic recursive gradient descent algorithm (called SSRGD) can find an $(\epsilon,\delta)$-second-order stationary point with $\widetilde{O}(\sqrt{n}/\epsilon^2 + \sqrt{n}/\delta^4 + n/\delta^3)$ stochastic gradient complexity for nonconvex finite-sum problems. As a by-product, SSRGD finds an $\epsilon$-first-order stationary point with $O(n+\sqrt{n}/\epsilon^2)$ stochastic gradients. These results are almost optimal since Fang et al. [2018] provided a lower bound $\Omega(\sqrt{n}/\epsilon^2)$ for finding even just an $\epsilon$-first-order stationary point. We emphasize that SSRGD algorithm for finding second-order stationary points is as simple as for finding first-order stationary points just by adding a uniform perturbation sometimes, while all other algorithms for finding second-order stationary points with similar gradient complexity need to combine with a negative-curvature search subroutine (e.g., Neon2 [Allen-Zhu and Li, 2018]). Moreover, the simple SSRGD algorithm gets a simpler analysis. Besides, we also extend our results from nonconvex finite-sum problems to nonconvex online (expectation) problems, and prove the corresponding convergence results. … **MedSim**

We present MedSim, a novel semantic SIMilarity method based on public well-established bio-MEDical knowledge graphs (KGs) and large-scale corpus, to study the therapeutic substitution of antibiotics. Besides hierarchy and corpus of KGs, MedSim further interprets medicine characteristics by constructing multi-dimensional medicine-specific feature vectors. Dataset of 528 antibiotic pairs scored by doctors is applied for evaluation and MedSim has produced statistically significant improvement over other semantic similarity methods. Furthermore, some promising applications of MedSim in drug substitution and drug abuse prevention are presented in case study. … **Fast and Robust Twin Support Vector Machine (FR-TSVM)**

Twin support vector machine~(TSVM) is a powerful learning algorithm by solving a pair of smaller SVM-type problems. However, there are still some specific issues waiting to be solved when it faces with some real applications, \emph{e.g}, low efficiency and noise data. In this paper, we propose a Fast and Robust TSVM~(FR-TSVM) to deal with these issues above. In FR-TSVM, we propose an effective fuzzy membership function to ease the effects of noisy inputs. We apply the fuzzy membership to each input instance and reformulate the TSVMs such that different input instances can make different contributions to the learning of the separating hyperplanes. To further speed up the training procedure, we develop an efficient coordinate descent algorithm with shirking to solve the involved a pair of quadratic programming problems (QPPs) of FR-TSVM. Moreover, theoretical foundations of the proposed model are analyzed in details. The experimental results on several artificial and benchmark datasets indicate that the FR-TSVM not only obtains the fast learning speed but also shows the robust classification performance.

➘ “Twin Support Vector Machine” …

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