Mahdi Shamsi

Mahdi Shamsi, Soosan Beheshti

Selecting a clustering algorithm and its hyperparameters without labels is a common difficulty in engineering machine learning pipelines that work with unsupervised analysis of sensor, image, or process data. Clustering validation indices (CVIs) provide internal scores for ranking candidate clusterings, but most popular CVIs are built from Euclidean compactness and separation terms and so tend to favour compact, convex partitions. Their performance is known to degrade on non convex, irregular, or variable density data, where kernel transformations or alternative distance measures are typically used at the cost of additional tuning and computation. This paper introduces the Central Description Length (CDL) clustering validation index. CDL uses the observed within cluster compactness, the estimated cluster centers, and the estimated cluster covariances to compute a probabilistic upper bound on the description length associated with the unobservable true cluster centers. The bound condenses intra cluster compactness and centroid displacement into a single computable quantity and is evaluated on the partition produced by any clustering algorithm. The implementation uses only observable quantities (the data, the partition, the estimated centers, and the estimated covariances) and does not use ground truth labels. On synthetic benchmarks with non convex and arbitrary shape clusters, CDL-CVI selected the reference number of clusters more often and reached higher Adjusted Rand Index (ARI) values than the conventional CVIs we tested, without an additional kernel preprocessing stage. On image benchmarks (MNIST, CIFAR-10, STL-10) clustered from frozen unsupervised embeddings, CDL-CVI returned cluster numbers close to the reference class counts across K-means, DBSCAN, and spectral clustering in the reported trials.

Naseh Majidi, Mahdi Shamsi, Farokh Marvasti

Price movement prediction has always been one of the traders' concerns in financial market trading. In order to increase their profit, they can analyze the historical data and predict the price movement. The large size of the data and complex relations between them lead us to use algorithmic trading and artificial intelligence. This paper aims to offer an approach using Twin-Delayed DDPG (TD3) and the daily close price in order to achieve a trading strategy in the stock and cryptocurrency markets. Unlike previous studies using a discrete action space reinforcement learning algorithm, the TD3 is continuous, offering both position and the number of trading shares. Both the stock (Amazon) and cryptocurrency (Bitcoin) markets are addressed in this research to evaluate the performance of the proposed algorithm. The achieved strategy using the TD3 is compared with some algorithms using technical analysis, reinforcement learning, stochastic, and deterministic strategies through two standard metrics, Return and Sharpe ratio. The results indicate that employing both position and the number of trading shares can improve the performance of a trading system based on the mentioned metrics.

Soosan Beheshti, Mahdi Shamsi

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially different complexities. Linear regression modeling is an important category of learning algorithms. The practical uncertainty of the target samples affects the generalization performance of the learned model. Failing to choose a proper model or hypothesis class can lead to serious issues such as underfitting or overfitting. These issues have been addressed by alternating cost functions or by utilizing cross-validation methods. These approaches can introduce new hyperparameters with their own new challenges and uncertainties or increase the computational complexity of the learning algorithm. On the other hand, the theory of probably approximately correct (PAC) aims at defining learnability based on probabilistic settings. Despite its theoretical value, PAC does not address practical learning issues on many occasions. This work is inspired by the foundation of PAC and is motivated by the existing regression learning issues. The proposed approach, denoted by epsilon-Confidence Approximately Correct (epsilon CoAC), utilizes Kullback Leibler divergence (relative entropy) and proposes a new related typical set in the set of hyperparameters to tackle the learnability issue. Moreover, it enables the learner to compare hypothesis classes of different complexity orders and choose among them the optimum with the minimum epsilon in the epsilon CoAC framework. Not only the epsilon CoAC learnability overcomes the issues of overfitting and underfitting, but it also shows advantages and superiority over the well known cross-validation method in the sense of time consumption as well as in the sense of accuracy.

Mahdi Shamsi, Soosan Beheshti

Support Vector Machine (SVM) is a robust machine learning algorithm with broad applications in classification, regression, and outlier detection. SVM requires tuning the regularization parameter (RP) which controls the model capacity and the generalization performance. Conventionally, the optimum RP is found by comparison of a range of values through the Cross-Validation (CV) procedure. In addition, for non-linearly separable data, the SVM uses kernels where a set of kernels, each with a set of parameters, denoted as a grid of kernels, are considered. The optimal choice of RP and the grid of kernels is through the grid-search of CV. By stochastically analyzing the behavior of the regularization parameter, this work shows that the SVM performance can be modeled as a function of separability and scatteredness (S&S) of the data. Separability is a measure of the distance between classes, and scatteredness is the ratio of the spread of data points. In particular, for the hinge loss cost function, an S&S ratio-based table provides the optimum RP. The S&S ratio is a powerful value that can automatically detect linear or non-linear separability before using the SVM algorithm. The provided S&S ratio-based table can also provide the optimum kernel and its parameters before using the SVM algorithm. Consequently, the computational complexity of the CV grid-search is reduced to only one time use of the SVM. The simulation results on the real dataset confirm the superiority and efficiency of the proposed approach in the sense of computational complexity over the grid-search CV method.

Mahdi Shamsi, Alireza Moslemi Haghighi, Farokh Marvasti

This paper considers the problem of detecting impaired and noisy nodes over network. In a distributed algorithm, lots of processing units are incorporating and communicating with each other to reach a global goal. Due to each one's state in the shared environment, they can help the other nodes or mislead them (due to noise or a deliberate attempt). Previous works mainly focused on proper locating agents and weight assignment based on initial environment state to minimize malfunctioning of noisy nodes. We propose an algorithm to be able to adapt sharing weights according to behavior of the agents. Applying the introduced algorithm to a multi-agent RL scenario and the well-known diffusion LMS demonstrates its capability and generality.

Mahdi Shamsi, Mahmoud Ghandi, Farokh Marvasti

Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, impulsive and Salt and Pepper noise removal problems. However, the challenges such as the speed of convergence and or the accuracy of the answer still remain. In order to improve the existing iterative algorithms, a non-linear method is discussed in this paper. The mentioned method is analyzed from different aspects, including its convergence and its ability to accelerate recursive algorithms. We show that this method is capable of improving Iterative Method (IM) as a non-uniform sampling reconstruction algorithm and some iterative sparse recovery algorithms such as Iterative Reweighted Least Squares (IRLS), Iterative Method with Adaptive Thresholding (IMAT), Smoothed l0 (SL0) and Alternating Direction Method of Multipliers (ADMM) for solving LASSO problems family (including Lasso itself, Lasso-LSQR and group-Lasso). It is also capable of both accelerating and stabilizing the well-known Chebyshev Acceleration (CA) method. Furthermore, the proposed algorithm can extend the stability range by reducing the sensitivity of iterative algorithms to the changes of adaptation rate.