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Inference in Graphical Models
, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor) ; Haji Mirsadeghi, Mir Omid (Supervisor)
Abstract
The purpose of this dissertation is to study issues in the field of graphical models.At the beginning, we will mention the main concepts of graphical models. Then we describe algorithms in exact inference. These algorithms are used to solve inferential issues and when the graph is related to the tree graph modeling. We also describe how these algorithms apply to non-tree graphs. In addition, we recall definitions such as cumulative function and set of mean parameters and important theorems applied in graphical models. Finally, we describe the important algorithms that are used to estimate the parameters in graphical models
Discrete Time vs Continuous Time Stock-price Dynamics and Implications for Option Pricing
, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor) ; Zamani, Shiva (Supervisor)
Abstract
In the present paper we construct stock price processes with the same marginal log- normal law as that of a geometric Brownian motion and also with the same transition density (and returns’ distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes’, in that option prices can be either arbitrarily close to the option intrinsic value or arbitrarily close to the underlying stock price. We also explain that this is due to the particular way one models the stock-price process in between the grid time instants which are relevant for trading
Image Categorization Using Deep Learning
, M.Sc. Thesis Sharif University of Technology ; Jafari Siavoshani, Mahdi (Supervisor) ; Rabiee, Hamid Reza (Co-Advisor)
Abstract
The representation of data influences the explanation factors of data variations. Thus,the success of learner algorithms depends on the data representation. Our main contribution in this thesis is learning of high level and abstract representation using deep structure. One of the fundamental examples of representation learning is the AutoEncoders. The auto-encoder is a rigid framework that doesn’t consider explanation factors in terms of statistical concepts. So, the auto-encoders can be re-interpreted by seeing the decoder as the statistical model of interest. The role of encoder is a mechanism for inference in the model described by the decoder. Our purpose is to design such model with...