We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, GLR-CUCB, which incorporates an efficient combinatorial semi-bandit algorithm, CUCB, with an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT). Our analysis shows that the regret of GLR-CUCB is upper bounded by O(√NKT log T), where N is the number of piecewise-stationary segments, K is the number of base arms, and T is the number of time steps. As a complement, we also derive a nearly matching regret lower bound on the order of Ω(√NKT), for both piecewise-stationary multi-armed bandits and combinatorial semi-bandits, using information-theoretic techniques and judiciously constructed piecewise-stationary bandit instances. Our lower bound is tighter than the best available regret lower bound, which is Ω(√T). Numerical experiments on both synthetic and real-world datasets demonstrate the superiority of GLR-CUCB compared to other state-of-the-art algorithms.
Neutrophils participate in the advancement of the human innate immune system and respond to perceived endogenous and exogenous threats. As a response mechanism, neutrophil extracellular traps (NETs) form near pathogens and surrounding tissues during an immune response. Drusen is an important marker of Age-Related Macular Degeneration (AMD) and plays an important role in the course of AMD. Aβ1-40 is the main component of drusen. However, the relationship between NETs and AMD or Aβ1-40 is unclear. Here, we found elevated levels of NETs in the serum of AMD patients and elevated levels in the serum of mouse models. We also observed the accumulation of neutrophils in the mouse retina. In addition, the production of NETs was inhibited by PAD4 inhibitors, which can alleviate chronic inflammation. Moreover, we confirmed that Aβ1-40 can induce NETs formation via the Toll-like receptor 4 (TLR4) and neutrophil NADPH oxidase (NOX) pathways. Our study confirmed that the formation of NETs is induced by Aβ1–40, and the results suggest that NETs may play a vital role in AMD pathogenesis.
We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, GLR-CUCB, which incorporates an efficient combinatorial semi-bandit algorithm, CUCB, with an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT). Our analysis shows that the regret of GLR-CUCB is upper bounded by O( √ N KT log T ), where N is the number of piecewise-stationary segments, K is the number of base arms, and T is the number of time steps. As a complement, we also derive a nearly matching regret lower bound on the order of Ω( √ N KT ), for both piecewise-stationary multi-armed bandits and combinatorial semi-bandits, using information-theoretic techniques and judiciously constructed piecewisestationary bandit instances. Our lower bound is tighter than the best available regret lower bound, which is Ω( √ T ). Numerical experiments on both synthetic and real-world datasets demonstrate the superiority of GLR-CUCB compared to other state-of-the-art algorithms.
We consider a problem that recovers a 2-D object and the underlying view angle distribution from its noisy projection tilt series taken at unknown view angles. Traditional approaches rely on the estimation of the view angles of the projections, which do not scale well with the sample size and are sensitive to noise. We introduce a new approach using the moment features to simultaneously recover the underlying object and the distribution of view angles. This problem is formulated as constrained nonlinear least squares in terms of the truncated Fourier-Bessel expansion coefficients of the object and is solved by a new alternating direction method of multipliers (ADMM)-based algorithm. Our numerical experiments show that the new approach outperforms the expectation maximization (EM)-based maximum marginalized likelihood estimation in efficiency and accuracy. Furthermore, the hybrid method that uses EM to refine ADMM solution achieves the best performance.
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