Sharif Digital Repository

In the era of the internet and with the emergence of online stores, the possibility of changing prices for these e-commerce platforms has become simple and virtually cost-free. This allows them to adjust prices optimally in response to environmental and surrounding factors, maximizing their revenue from product sales. This development has led to numerous applications of statistical learning methods, particularly online learning, in these markets. In this thesis, we explore the issue of online pricing from various perspectives. One aspect is that product pricing is based on their features, which can be numerous. This leads us to the use of online learning methods and statistical learning in... 

In this thesis, we are going to study the consistency properties of one of the most well-known linear estimators – LASSO estimator. First, we bring up some necessary background for introducing this estimator. Then, we are able to introduce primary and secondary forms of LASSO estimator. After that, we prove that primary form of the LASSO estimator is weakly consistent under certain weak conditions. We, also, prove a much stronger statement about the secondary form. We prove that the secondary form is strongly consistent. What’s more, with extra assumptions, we specify the convergence rate of the estimator. Finally, we propose a method for determining free parameter of primary form of LASSO,... 

We consider a biased random walk Xn on a Galton-watson tree with leaves in the subballistic regime. We prove that there exists an explicit constant ϒ = ϒ(β) ε (0,1),such that |Xn| is of order n. If Δn be the hitting time of level n, we prove that Δn{n1{ is tight. More ever we show thatΔn{n1{ does not converge in law. We prove that along the sequences npkq Xk\ , Δn{n1{ converges to certain infinity divisible laws. Key tools for the proof are the classical Harris decomposition for Galton-Watson trees, a new variant of regeneration times and the careful analysis of triangular arrays of i.i.d. random variables  

Sometimes, the relationship between two random variables is not a correlation, but, a causal relationship where only changes in one of the two variables can lead to changes in the second one. The importance of examining such cause-effect relationships lies in the fact that sometimes, beyond just knowing the correlation between two variables, we are looking for an active effect on one, and knowing whether or not other correlated variables will also change with the change of this variable is of key importance. Such a process of exploring and analyzing cause-effect relationships is called causal learning. Based on this, in this thesis, we will first review the methods of causal inference, as... 

In this thesis, we consider the model of random interlacement on transient graghs, which was first introduced by Sznitman for the special case of Zd(d > 3) in 2010’s. in Sznitman’s case, it was shown that on Zd: for any intensity u > 0, the interlacement set is almost surely connected. The main result of this thesis says that for transient, transitive graphs, the above property holds if and only if the graph is amenable. In paticular, we show that in nonamenable transitive graphs, for small values of the intensity u the interlacement set has infinitely many infinite clusters. We also provide examples of nonamenable transitive graphs, for which the interlacement set becomes connected for... 

In this thesis we introduce the objective method for solving combinatorial probability problems and combinatorial optimization. For introducing this method, we consider its application in solving problems such as graphs maximal partial matching problem. Then we introduce mean-field model, which has a close relationship with this method. Finally we use this method to discuss perfect mathching with minimal cost in complete graphs, and using obtaind theorems and concepts from solving this problem, like involution invariance and standard construction, we find an answer for random assigment problem, which is one of the most practical problems in the class of optimization problems  

In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)—the expected fraction of false discoveries among all discoveries—is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in... 

To reduce customer waiting times in various service conditions, admission control and service speedup can be implemented during times of congestion. In a healthcare setting, this may result in a patient being redirected to an alternative treatment facility. Additionally, waiting for patients can have negative impacts on their health and controlling population density can be costly. Implementing these measures may also take too much time or deviate from the ideal treatment. In this thesis, we will evaluate multi-server queuing systems by considering both speed and admission control simultaneously. We will use dynamic programming to determine the optimal control characteristics and calculate... 

In this dissertation, we investigate the problem of the existence of finite geodetic sequences from point to point (0, n). This has not been proven in the general case. In this dissertation, we present an article that illustrates this question in a particular case of z ^ 2 subspaces whose self and complement are infinite and connected (e.g., slit planes, half-planes, and sectors). Writing x_n for the sequence of boundary vertices, we show that the sequence of geodesics from any point to x_n has an almost sure limit assuming only existence of finite geodesics. For all passage-time configurations, we show existence of a limiting Busemann function. Specializing to the case of the half-plane, we... 

In today’s world, large internet companies carry a lot of data. The tests with low triggering rate are designed for causal inference. By regarding the economic scale of Internet companies and high decision -making speeds, it is essential to use variance reduction methods to estimate the causal effect of treatment with sufficient precision. To this goal, the trigger- dilute analysis method is designed and used. When it comes to partial triggering, the stimulation analysis method loses its efficiency, so a new replacement method is designed in which an unbiased estimation along with the reduction of variance is presented to estimate ITT within one-way experiments. This method is based on the... 

Networks and the epidemiology of directly transmitted infectious diseases are fun-damentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a network. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections.Motivated by the analysis of social networks, we study a model of random net-works that has both a given degree distribution and a tunable clustering coefficient.We consider two... 

In this thesis we try to understand one of the most important subfield of deep learning, the generative adversarial networks. In this framework the goal is to reach a generator that generates samples from a target distribution. The target distribution is usually su- per high dimensional and we only have sample access to it. primarily , this distribution was used to be for set of Images (e.g. images of celebrity faces) and GANs performed well in this setting. In this framework two models work simultaneously: a generator tries to generate realistic samples from the target distribution and a discriminator or critic tries to distinguish real samples from generated (fake) samples or more... 

Given two stationary random measures on Rd, we study transport kernels between them that are translation-covariant. We will provide an algorithm that constructs such a transport kernel, with some assumption on their intensities. As a result, this algorithm can be used to construct the Palm version of an ergodic random measure by simply applying a (random) translation and vice versa, to reconstruct the distribution of the random measure from its Palm distribution. Given realizations of the two random measures, our algorithm provides its result in a deterministic way. The existence of such transport kernels is proved in [18] in an abstract way. Nevertheless, there has been tremendous interest... 

A perturbed lattice is a point process π={x+Y_x ∶x ∈Z^d} where the lattice points in Z^d are perturbed by i.i.d . random variables {Y_x }_(x∈Z^d ). A random point process π is said to be rigid if π∩B_1 (0) , the number of points in a ball , can be exactly determined given π∩B_1^c (0) , the points outside the ball . The process π is called deletion tolerant if removing one point of π yields a process with distribution indistinguishable from that of π . Suppose that Y_x~N_d (0,σ^2 I) are Gaussian vectors with d independent components of variance σ^2 . Holroyd and Soo showed that in dimensions d = 1 , 2 the resulting Gaussian perturbed lattice π is rigid and deletion... 

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  

Housing is one of the important staple goods. The main different between housing market and the other markets is limitation of stock at short term. So it is very important to regularize housing market for apropos accountability and according to society consumption demand. This document introduce the result of an agent based modeling of housing market. There are agents that find out the maximum utility for choosing one of following house related conditions: purchase, sale and lease agreement. In fact in this model people have two phases. The effect of land value taxation for regularization of housing market will analyses with this model. Its seems that by implementation of mentioned tax, the... 

We study the problem of preclustering a set $B$ of imprecise points in~$\Reals^d$: we wish to cluster the regions specifying the potential locations of the points such that, no matter where the points are located within their regions, the resulting clustering approximates the optimal clustering for those locations. We consider $k$-center, $k$-median, and $k$-means clustering, and obtain the various results. Then we study the higher order Voronoi Tessellations as an important concept in clustering area. Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in $\Reals^2$ to $\Reals^3$, we get precise relations in terms of Morse theoretic quantities... 

Let be a sub-semigroup of SL(d;Z) which acts strongly irreducible on Rd, i.e. there is not any invariant finite union of nontrivial proper subspaces of Rd. acts on Td by homeomorphisms. We will show that under these assumptions every infinite invariant subset of Td under the action of is dense in Td. For instance, if x is a point in Td which is not rational, then x = Td. In this thesis, we will follow the method of Y. Benoist and J.F. Quint for proving such results. Their method is to prove some kind of rigidity for the stationary measures for the action of on Td. Actually, every atomless stationary measure is the lebesgue measure on Td which is invariant under all the elements of... 

We study the expected value of stopping times in stochastic processes. Since there is no rigorous solution for computing stopping times in many processes, our approach is based on estimation using well-known methods in the Reinforcement Learning literature. The primary method in this research is the temporal difference algorithm. With some modifications, we can study the role of some state features in determining the stopping time. Moreover, without a complicated mathematical analysis, we can find functions closely enough to the goal function.Furthermore, we compare our proposed algorithm to the well-known regression methods and show our algorithm's advantages and disadvantages. The primary... 

Solving the visual symbol grounding problem has long been a goal of modern aritificial intelligence. Due to recent breakthroughs in deep learning methods for natural language processing and visual interpretation tasks‚ the field now seems to be as near to achieving this goal as it ever was. Also recent progress in using recurrent neural netowrks (RNNs) for image description‚ has motivated the exploration of their application for video description tasks. However, while images remain static‚ interpreting videos require modeling complex dynamic temporal sturctures and then properly integrating that information into a natural language description. Recurrent neural networks can be both used to...