scholarly journals Efficient Inexact Proximal Gradient Algorithm for Nonconvex Problems

2017 ◽  
Author(s):  
Quanming Yao ◽  
James T. Kwok ◽  
Fei Gao ◽  
Wei Chen ◽  
Tie-Yan Liu
Keyword(s):  
Matrix Completion ◽  
Closed Form Solution ◽  
Image Inpainting ◽  
Form Solution ◽  
The State ◽  
Gradient Algorithm ◽  
Nonconvex Problems ◽  
Proximal Gradient Algorithm ◽  
Comparable Performance ◽  
Completion Problems

While proximal gradient algorithm is originally designed for convex optimization, several variants have been recently proposed for nonconvex problems. Among them, nmAPG [Li and Lin, 2015] is the state-of-art. However, it is inefficient when the proximal step does not have closed-form solution, or such solution exists but is expensive, as it requires more than one proximal steps to be exactly solved in each iteration. In this paper, we propose an efficient accelerate proximal gradient (niAPG) algorithm for nonconvex problems. In each iteration, it requires only one inexact (less expensive) proximal step. Convergence to a critical point is still guaranteed, and a O(1/k) convergence rate is derived. Experiments on image inpainting and matrix completion problems demonstrate that the proposed algorithm has comparable performance as the state-of-the-art, but is much faster.

scholarly journals Robustness Can Be Cheap: A Highly Efficient Approach to Discover Outliers under High Outlier Ratios

2019 ◽  
Vol 33 ◽  
pp. 5313-5320
Author(s):  
Siqi Wang ◽  
En Zhu ◽  
Xiping Hu ◽  
Xinwang Liu ◽  
Qiang Liu ◽  
...  
Keyword(s):  
Computational Cost ◽  
Solution Process ◽  
Closed Form Solution ◽  
Form Solution ◽  
Low Rank ◽  
Alternative Formulation ◽  
Efficient Detection ◽  
Comparable Performance ◽  
High Space ◽  
High Outlier

Efficient detection of outliers from massive data with a high outlier ratio is challenging but not explicitly discussed yet. In such a case, existing methods either suffer from poor robustness or require expensive computations. This paper proposes a Low-rank based Efficient Outlier Detection (LEOD) framework to achieve favorable robustness against high outlier ratios with much cheaper computations. Specifically, it is worth highlighting the following aspects of LEOD: (1) Our framework exploits the low-rank structure embedded in the similarity matrix and considers inliers/outliers equally based on this low-rank structure, which facilitates us to encourage satisfying robustness with low computational cost later; (2) A novel re-weighting algorithm is derived as a new general solution to the constrained eigenvalue problem, which is a major bottleneck for the optimization process. Instead of the high space and time complexity (O((2n)2)/O((2n)3)) required by the classic solution, our algorithm enjoys O(n) space complexity and a faster optimization speed in the experiments; (3) A new alternative formulation is proposed for further acceleration of the solution process, where a cheap closed-form solution can be obtained. Experiments show that LEOD achieves strong robustness under an outlier ratio from 20% to 60%, while it is at most 100 times more memory efficient and 1000 times faster than its previous counterpart that attains comparable performance. The codes of LEOD are publicly available at https://github.com/demonzyj56/LEOD.

scholarly journals Interpretable Drug Target Predictions using Self-Expressiveness

2021 ◽  
Author(s):  
Diego Galeano ◽  
Santiago Noto ◽  
Ruben Jimenez ◽  
Alberto Paccanaro
Keyword(s):  
Drug Target ◽  
Drug Targets ◽  
Prediction Models ◽  
Matrix Completion ◽  
Closed Form Solution ◽  
Target Prediction ◽  
Form Solution ◽  
Protein Targets ◽  
Drug Target Prediction ◽  
Similarity Matrices

AbstractThe identification of missing drug targets is critical for the development of treatments and for the molecular elucidation of drug side effects. Drug targets have been predicted by exploiting molecular, biological or pharmacological features of drugs and protein targets. Yet, developing integrative and interpretable machine learning models for predicting drug targets remains a challenging task. We present Inception, an integrative and interpretable matrix completion model for predicting drug targets. Inception is a self-expressive model that learns two similarity matrices: one for drugs and another for protein targets. These learned similarity matrices are key for our models’ interpretability: they can explain how a predicted drug-target interaction can be explain in terms of a linear combination of chemical, biological and pharmacological similarities. We develop a novel objective function with efficient closed-form solution. To demonstrate the ability of Inception at recovering missing drug-target interactions (DTIs), we perform cross-validation experiments with stringent controls of data imbalance, chemical similarities between drugs and sequence similarities between targets. We also assess the performance of our model using a simulated prospective approach. Having trained our model with DTIs from a snapshot 2011 of the DrugBank database, we test whether we could predict DTIs from a 2020 snapshot of DrugBank. Inception outperforms two state-of-the-art drug target prediction models in all the scenarios. This suggests that Inception could be useful for predicting missing drug target interactions while providing interpretable predictions.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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