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On statistical learning of simplices: Unmixing problem revisited
, Article Annals of Statistics ; Volume 49, Issue 3 , 2021 , Pages 1626-1655 ; 00905364 (ISSN) ; Ilchi, S ; Saberi, A. H ; Motahari, S. A ; Hossein Khalaj, B ; Rabiee, H. R ; Sharif University of Technology
Institute of Mathematical Statistics
2021
Abstract
We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of “spectral unmixing.” We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of ε is O(Kε2 log Kε ), which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets...
Application of Semi-Supervised Learning in Image Processing
, M.Sc. Thesis Sharif University of Technology ; Rabiee, Hamidreza (Supervisor)
Abstract
In recent years, the emergence of semi-supervised learning methods has broadened the scope of machine learning, especially for pattern classification. Besides obviating the need for experts to label the data, efficient use of unlabeled data causes a significant improvement in supervised learning methods in many applications. With the advent of statistical learning theory in the late 80's, and the emergence of the concept of regularization, kernel learning has always been in deep concentration. In recent years, semi-supervised kernel learning, which is a combination of the two above-mentioned viewpoints, has been considered greatly.
Large number of dimensions of the input data along with...
Large number of dimensions of the input data along with...
Fundamental Bounds for Clustering of Bernoulli Mixture Models
, M.Sc. Thesis Sharif University of Technology ; Motahari, Abolfazl (Supervisor)
Abstract
A random vector with binary components that are independent of each other is referred to as a Bernoulli random vector. A Bernoulli Mixture Model (BMM) is a combination of a finite number of Bernoulli models, where each sample is generated randomly according to one of these models. The important challenge is to estimate the parameters of a Bernoulli Mixture Model or to cluster samples based on their source models. This problem has applications in bioinformatics, image recognition, text classification, social networks, and more. For example, in bioinformatics, it pertains to clustering ethnic groups based on genetic data. Many studies have introduced algorithms for solving this problem without...
Sparsity and infinite divisibility
, Article IEEE Transactions on Information Theory ; Volume 60, Issue 4 , 2014 , Pages 2346-2358 ; ISSN: 00189448 ; Unser, M ; Sharif University of Technology
Abstract
We adopt an innovation-driven framework and investigate the sparse/compressible distributions obtained by linearly measuring or expanding continuous-domain stochastic models. Starting from the first principles, we show that all such distributions are necessarily infinitely divisible. This property is satisfied by many distributions used in statistical learning, such as Gaussian, Laplace, and a wide range of fat-tailed distributions, such as student's-t and α-stable laws. However, it excludes some popular distributions used in compressed sensing, such as the Bernoulli-Gaussian distribution and distributions, that decay like exp (-O(|x|p)) for 1 < p < 2. We further explore the implications of...
Using empirical covariance matrix in enhancing prediction accuracy of linear models with missing information
, Article 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017, 3 July 2017 through 7 July 2017 ; 2017 , Pages 446-450 ; 9781538615652 (ISBN) ; Shahsavari, S ; Esmaeili, A ; Marvasti, F ; Sharif University of Technology
Abstract
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing...
A biologically plausible learning method for neurorobotic systems
, Article 2009 4th International IEEE/EMBS Conference on Neural Engineering, NER '09, Antalya, 29 April 2009 through 2 May 2009 ; 2009 , Pages 128-131 ; 9781424420735 (ISBN) ; Vosoughi Vahdat, B ; National Institutes of Health, NIH; National Institute of Neurological Disorders and Stroke, NINDS; National Science Foundation, NSF ; Sharif University of Technology
2009
Abstract
This paper introduces an incremental local learning algorithm inspired by learning in neurobiological systems. This algorithm has no training phase and learns the world during operation, in a lifetime manner. It is a semi-supervised algorithm which combines soft competitive learning in input space and linear regression with recursive update in output space. This method is also robust to negative interference and compromises bias-variance dilemma. These qualities make the learning method a good nonlinear function approximator having possible applications in neuro-robotic systems. Some simulations illustrate the effectiveness of the proposed algorithm in function approximation, time-series...
An efficient hardware implementation for a motor imagery brain computer interface system
, Article Scientia Iranica ; Volume 26, Issue 1 , 2019 , Pages 72-94 ; 10263098 (ISSN) ; Mohammadzade, H ; Chamanzar, A. R ; Shabany, M ; Ghojogh, B ; Sharif University of Technology
Sharif University of Technology
2019
Abstract
Brain Computer Interface (BCI) systems, which are based on motor imagery, enable humans to command artificial peripherals by merely thinking about the task. There is a tremendous interest in implementing BCIs on portable platforms, such as Field Programmable Gate Arrays (FPGAS) due to their low-cost, low-power and portability characteristics. This article presents the design and implementation of a Brain Computer Interface (BCI) system based on motor imagery on a Virtex-6 FPGA. In order to design an accurate algorithm, the proposed method avails statistical learning methods such as Mutual Information (MI), Linear Discriminant Analysis (LDA), and Support Vector Machine (SVM). It also uses...
An efficient hardware implementation for a motor imagery brain computer interface system
, Article Scientia Iranica ; Volume 26, Issue 1 , 2019 , Pages 72-94 ; 10263098 (ISSN) ; Mohammadzade, H ; Chamanzar, A ; Shabany, M ; Ghojogh, B ; Sharif University of Technology
Sharif University of Technology
2019
Abstract
Brain Computer Interface (BCI) systems, which are based on motor imagery, enable humans to command artificial peripherals by merely thinking about the task. There is a tremendous interest in implementing BCIs on portable platforms, such as Field Programmable Gate Arrays (FPGAS) due to their low-cost, low-power and portability characteristics. This article presents the design and implementation of a Brain Computer Interface (BCI) system based on motor imagery on a Virtex-6 FPGA. In order to design an accurate algorithm, the proposed method avails statistical learning methods such as Mutual Information (MI), Linear Discriminant Analysis (LDA), and Support Vector Machine (SVM). It also uses...