Convergence of Unregularized Online Learning Algorithms

In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess generalization errors in expectation. A sufficient condition for the almost sure convergence is also given. With high probability, we provide explicit convergence rates of the excess generalization errors for both averaged iterates and the last iterate, which in turn also imply convergence rates with probability one. To our best knowledge, this is the first high-probability convergence rate for the last iterate of online gradient descent algorithms without strong convexity. Without any boundedness assumptions on iterates, our results are derived by a novel use of two measures of the algorithm's one-step progress, respectively by generalization errors and by distances in RKHSs, where the variances of the involved martingales are cancelled out by the descent property of the algorithm

Learning from networked examples

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may share some common objects, and hence share the features of these shared objects. We show that the classic approach of ignoring this problem potentially can have a harmful effect on the accuracy of statistics, and then consider alternatives. One of these is to only use independent examples, discarding other information. However, this is clearly suboptimal. We analyze sample error bounds in this networked setting, providing significantly improved results. An important component of our approach is formed by efficient sample weighting schemes, which leads to novel concentration inequalities

Online Regularized Learning Algorithm for Functional Data

In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning algorithm for functional linear models in reproducing kernel Hilbert spaces. Convergence analysis of excess prediction error and estimation error are provided with polynomially decaying step-size and constant step-size, respectively. Fast convergence rates can be derived via a capacity dependent analysis. By introducing an explicit regularization term, we uplift the saturation boundary of unregularized online learning algorithms when the step-size decays polynomially, and establish fast convergence rates of estimation error without capacity assumption. However, it remains an open problem to obtain capacity independent convergence rates for the estimation error of the unregularized online learning algorithm with decaying step-size. It also shows that convergence rates of both prediction error and estimation error with constant step-size are competitive with those in the literature.Comment: 32 page

MicroRNA-9-5p functions as a tumor suppressor in prostate cancer via targeting UTRN

Accumulating evidence indicates that miR-9-5p plays an important role in several diseases, especially tumor progression. In this study, we investigated the clinical significance and biological function of miR-9-5p in prostate cancer (PCa). Using quantitative real time PCR (qRT-PCR) analysis, we found miR-9-5p level was significantly down-regulated in PCa tissues and cell lines. The decreased miR-9-5p expression was associated with tumor size, preoperative PSA, Gleason score and lymph node metastasis. Kaplan-Meier survival analysis showed patients with low level of miR-9-5p had significantly decreased rates of overall survival (OS). Multivariate analyses showed that miR-9-5p was an independent predictor of PCa patients’ prognosis. Through CCK-8 and Transwell assays, miR-9-5p overexpression by miR-9-5p mimics transfection was demonstrated to suppress the proliferation, migration and invasion of PCa cells. Mechanistically, luciferase reporter assay, qRT-PCR and Western blot demonstrated that Utrophin (UTRN) is a direct target of miR-9-5p in PCa cells. The status of UTRN protein in PCa tissues was much higher than that in adjacent tissues by immunohistochemical staining and its mRNA levels were inversely correlated with miR-9-5p in PCa tissues. Importantly, UTRN knockdown by siUTRN imitated the suppressive effects of miR-9-5p on cell proliferation, migration and invasion in PCa. In summary, miR-9-5p might novel prognostic biomarker in and targeting UTRN by miR-9-5p could be potential therapeutic candidates for PCa

Targeting Integrin-β1 Impedes Cytokine-Induced Osteoclast Differentiation: A Potential Pharmacological Intervention in Pathological Osteolysis

Purpose: To examine whether integrin-β1 is essential for osteoclast differentiation and function and if it can be targeted for pharmacological intervention in pathological osteolysis.Methods: Control and Integrin-β1 knockdown RAW 264.7 cells were treated with receptor activator of nuclear factor kappa-B (RANKL) or TNF-α and evaluated for osteoclast differentiation. Osteoclast differentiation and function were evaluated by marker protein analysis, tartrate-resistant acid phosphatase (TRAP) and resorption assays. Furthermore, downstream molecular signaling analysis was probed using small molecule inhibitors and blocking antibodies, and evaluated by immunoblotting.Results: Integrin-β1 knockdown cells showed reduced osteoclast differentiation following TNF-α treatment while no change was seen after RANKL treatment (p < 0.05). Immunoblot-based molecular signaling analysis showed involvement of MAPK kinase signaling in mediating TNF-α/integrin-β1- induced osteoclastogenesis. Finally, when MAPK kinase inhibitor (2.5 and 5 μM; p < 0.05) and integrin- β1 blocking antibody (2.5 and 5 μg/mL; p < 0.05) was used to specifically attenuate TNF-α induced osteoclastogenesis, no change was observed in RANKL-induced osteoclast formation.Conclusion: The data obtained highlight the role of integrin-β1 in TNF-α-induced osteoclastogenesis, but not in RANKL pathway. Given that, inflammatory cytokine secretions such as TNF-α are progressively implicated in pathological osteolysis, targeting this pathway may attenuate osteolysis in pathological bone tissues.Keywords: Osteoclast differentiation, Integrin-β1, Receptor activator of nuclear factor kappa-B, TNFalpha, Mitogen activated protein kinase, Cytokines, Skeletal diseas