Sharif Digital Repository

In traditional machine learning approaches to classification, one uses only a labeled set to train the classifier. Labeled instances however are often difficult, expensive, or time consuming to obtain, as they require the efforts of experienced human annotators. Meanwhile unlabeled data may be relatively easy to collect, but there has been few ways to use them. Semi-supervised learning addresses this problem by using large amount of unlabeled data, together with the labeled data, to build better classifiers. Because semi-supervised learning requires less human effort and gives higher accuracy.Formally, this intuition corresponds to estimating a label function f on the graph so that it... 

In this thesis, we study image restoration problems, which can be modeled as inverse problems. Our main focus is on inverse problems with Poisson noise; which are useful in many problems like positron emission tomography, fluorescence microscopy, and astronomy imaging. As a popular method in the literature, we use statistic modeling of inverse problem with Poisson noise, in the MAP-estimation framework. Then we introduce a semi-implicit minimization method, FB-EM-TV, that involves two alternate steps, including an EM step and a weighted ROF problem. Then we study well-posedness, existence and stability of the solution. This method can be interpreted as a forward-backward splitting strategy,... 

As application demands for online convex optimization accelerate, the need for design-ing new methods that simultaneously cover a large class of convex functions and im-pose the lowest possible regret is highly rising. Known online optimization methods usually perform well only in specific settings, e.g., specific parameters such as the diam-eter of decision space, Lipschitz constant, and strong convexity coefficient, where their performance depends highly on the geometry of the decision space and cost functions. However, in practice, the lack of such geometric information leads to confusion in using the appropriate algorithm. To address these issues, some adaptive methods have been proposed... 

Exact Renormalization Equations (ERGE) are powerful non-perturbative tools to study the dynamics of Quantum Field theories, with respect to the change of energy. Putting cut-off on momentums of the system, is the specific regularization that is used to obtain ERGEs. This regularization breaks the gauge symmetry in the case of gauge theories. So the symmetry will be lost through the energy flow as well.Finding a gauge symmetry for a regularized system is the aim of this research. Also we have investigated the related ERGEs and the behavior of symmetry through the flow  

Reinforcement learning is a successful model of learning that has received a lot of attention in recent years and has had significant achievements. However, methods based on reinforcement require a lot of data. Therefore, it is important to find ideas to keep learning at a high level despite the lack of data. Many of these ideas are known as statistical regularity. In this thesis, we study methods to enhance the learning rate, including methods for sharing neural network weights between value function and policy networks. In this thesis we will try to gain a more general understanding of the regularization in reinforcement learning and increase the learning rate by implementing these methods... 

Deep Neural Networks, are predictive models in Machine Learning, that during the last decade they've had a great success. However being in an over-parametrized and highly non-convex regime, the analytical examinations of these models is quite a challenging task to do. The empirical developments of Neural Networks, and their distinguishing performance in prediction problems, has motivated researchers, to formalize a theoretical foundations for these models and provide us with a framework, in which one can explain and justify their behavior and properties. this framework is of great importance because it would help us to come to a better understanding of how these models work and also enables... 

Speaker verification as a kind of biometric methods aims to verify the identity of a person from characteristics of their voice. This method faces many challenges such as voice imitation (spoofing), use of recorded voice, high sensitivity to convolutive distortions resulted by channel, and a large performance degradation for short-duration utterances. The aim of this thesis is to propose different methods for reducing the effects of non-identity information,especially the channel, and also solving the problem of new methods for text-dependent speaker verification with very short utterances. i-vector has been the best speaker modeling method in recent years but it doesn’t result in good... 

Graph signals are sets of values residing on sets of nodes that are connected via edges. Graph Neural Networks (GNNs) are a type of machine learning model for working with graph-structured data, such as graph signals. GNNs have applications in graph classification, node classification, and link prediction. They can be thought of as learnable filters. In this thesis, our focus is on graph filters and enhancing the performance of GNNs. In the first part, we aim to reduce computational costs in graph signal processing, particularly in graph filters. We explore methods to transform signals to the frequency domain with lower computational cost. In the latter part, we examine regulations in... 

One of the major challenges in artificial intelligence is the presence of imbalanced data. Imbalanced data occurs when the number of samples in some classes is significantly lower than in others. This imbalance can lead to bias in machine learning models, as models tend to learn better and more accurately from classes with more samples. As a result, they may perform poorly when classifying samples from minority classes. This issue becomes particularly important when minority classes play a critical role in sensitive applications such as healthcare or security. In these cases, it is essential to pay close and fair attention to the minority classes to avoid unjust outcomes. In recent years,...