367 research outputs found
Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret
We investigate a generalized framework for estimating latent low-rank tensors
in an online setting, encompassing both linear and generalized linear models.
This framework offers a flexible approach for handling continuous or
categorical variables. Additionally, we investigate two specific applications:
online tensor completion and online binary tensor learning. To address these
challenges, we propose the online Riemannian gradient descent algorithm, which
demonstrates linear convergence and the ability to recover the low-rank
component under appropriate conditions in all applications. Furthermore, we
establish a precise entry-wise error bound for online tensor completion.
Notably, our work represents the first attempt to incorporate noise in the
online low-rank tensor recovery task. Intriguingly, we observe a surprising
trade-off between computational and statistical aspects in the presence of
noise. Increasing the step size accelerates convergence but leads to higher
statistical error, whereas a smaller step size yields a statistically optimal
estimator at the expense of slower convergence. Moreover, we conduct regret
analysis for online tensor regression. Under the fixed step size regime, a
fascinating trilemma concerning the convergence rate, statistical error rate,
and regret is observed. With an optimal choice of step size we achieve an
optimal regret of . Furthermore, we extend our analysis to the
adaptive setting where the horizon T is unknown. In this case, we demonstrate
that by employing different step sizes, we can attain a statistically optimal
error rate along with a regret of . To validate our theoretical
claims, we provide numerical results that corroborate our findings and support
our assertions
Provable Sample-Efficient Sparse Phase Retrieval Initialized by Truncated Power Method
We study the sparse phase retrieval problem, recovering an -sparse
length- signal from magnitude-only measurements. Two-stage non-convex
approaches have drawn much attention in recent studies for this problem.
Despite non-convexity, many two-stage algorithms provably converge to the
underlying solution linearly when appropriately initialized. However, in terms
of sample complexity, the bottleneck of those algorithms often comes from the
initialization stage. Although the refinement stage usually needs only
measurements, the widely used spectral initialization in
the initialization stage requires measurements to produce
a desired initial guess, which causes the total sample complexity order-wisely
more than necessary. To reduce the number of measurements, we propose a
truncated power method to replace the spectral initialization for non-convex
sparse phase retrieval algorithms. We prove that
measurements, where is the stable sparsity of the underlying signal,
are sufficient to produce a desired initial guess. When the underlying signal
contains only very few significant components, the sample complexity of the
proposed algorithm is and optimal. Numerical experiments
illustrate that the proposed method is more sample-efficient than
state-of-the-art algorithms
Dynamic Multi-Arm Bandit Game Based Multi-Agents Spectrum Sharing Strategy Design
For a wireless avionics communication system, a Multi-arm bandit game is
mathematically formulated, which includes channel states, strategies, and
rewards. The simple case includes only two agents sharing the spectrum which is
fully studied in terms of maximizing the cumulative reward over a finite time
horizon. An Upper Confidence Bound (UCB) algorithm is used to achieve the
optimal solutions for the stochastic Multi-Arm Bandit (MAB) problem. Also, the
MAB problem can also be solved from the Markov game framework perspective.
Meanwhile, Thompson Sampling (TS) is also used as benchmark to evaluate the
proposed approach performance. Numerical results are also provided regarding
minimizing the expectation of the regret and choosing the best parameter for
the upper confidence bound
Investigating the Impact of Corporate Governance on the Relationship between Related Party Transactions and Earning Management: Empirical Evidence from Chinese Private Listed Companies
Abstract
Earnings manipulation and related party transactions (RPT) are common problems and hot topics in earlier academic research. The prior literature on the relationship between RPT and earning management (EM) has developed mature and comprehensive. However, previous empirical research on the relationship between RPT and EM lack considering the concept of CG. Therefore, this research refer CG quality to further analyze and discuss the relationship between RPT and accrual-based EM. The purpose of this research is to analyze the relationship between related party transactions and earning management, and further discuss the impact of different corporate governance environments on the relationship between related party transactions and earnings management in Chinese private listed companies. This research utilizes quantitative research method to analyze the issue between RPT, EM and CG based on the data of 1134 private listed companies from 2016 to 2018. This research uses modify Jones model to measure the level of accrual-based EM and constructs CG index by combining five factors of CG to measure the quality of CG. The results prove that there is a positive relationship between RPT and EM, and the quality of CG has a negative impact on the relationship between RPT and EM. This means that good corporate governance environment helps to alleviate the relationship between RPT and EM. Therefore, management and regulators should pay more attention to establishing a more complete corporate governance system to fundamentally alleviate and improve improper connected transactions and earnings management behavior, whatever from the perspective of the company or the capital market supervision.
Key words: related party transactions; earning management; corporate governance; Chinese private listed companie
Nonconvex Stochastic Bregman Proximal Gradient Method with Application to Deep Learning
The widely used stochastic gradient methods for minimizing nonconvex
composite objective functions require the Lipschitz smoothness of the
differentiable part. But the requirement does not hold true for problem classes
including quadratic inverse problems and training neural networks. To address
this issue, we investigate a family of stochastic Bregman proximal gradient
(SBPG) methods, which only require smooth adaptivity of the differentiable
part. SBPG replaces the upper quadratic approximation used in SGD with the
Bregman proximity measure, resulting in a better approximation model that
captures the non-Lipschitz gradients of the nonconvex objective. We formulate
the vanilla SBPG and establish its convergence properties under nonconvex
setting without finite-sum structure. Experimental results on quadratic inverse
problems testify the robustness of SBPG. Moreover, we propose a momentum-based
version of SBPG (MSBPG) and prove it has improved convergence properties. We
apply MSBPG to the training of deep neural networks with a polynomial kernel
function, which ensures the smooth adaptivity of the loss function.
Experimental results on representative benchmarks demonstrate the effectiveness
and robustness of MSBPG in training neural networks. Since the additional
computation cost of MSBPG compared with SGD is negligible in large-scale
optimization, MSBPG can potentially be employed as an universal open-source
optimizer in the future.Comment: 37 page
Distributed Power System Virtual Inertia Implemented by Grid-Connected Power Converters
Renewable energy sources (RESs), e.g., wind and solar photovoltaics, have been increasingly used to meet worldwide growing energy demands and reduce greenhouse gas emissions. However, RESs are normally coupled to the power grid through fast-response power converters without any inertia, leading to decreased power system inertia. As a result, the grid frequency may easily go beyond the acceptable range under severe frequency events, resulting in undesirable load-shedding, cascading failures, or even large-scale blackouts. To address the ever-decreasing inertia issue, this paper proposes the concept of distributed power system virtual inertia, which can be implemented by grid-connected power converters. Without modifications of system hardware, power system inertia can be emulated by the energy stored in the dc-link capacitors of grid-connected power converters. By regulating the dc-link voltages in proportional to the grid frequency, the dc-link capacitors are aggregated into an extremely large equivalent capacitor serving as an energy buffer for frequency support. Furthermore, the limitation of virtual inertia, together with its design parameters, is identified. Finally, the feasibility of the proposed concept is validated through simulation and experimental results, which indicate that 12.5% and 50% improvements of the frequency nadir and rate of change of frequency can be achieved.NRF (Natl Research Foundation, S’pore)Accepted versio
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