9 skills found
jkirkby3 / PymleMaximum Likelihood estimation and Simulation for Stochastic Differential Equations (Diffusions)
utkarshsrivastava / ParallelSparseMatrixFactorizationSparse Matrix Factorization (SMF) is a key component in many machine learning problems and there exist a verity a applications in real-world problems such as recommendation systems, estimating missing values, gene expression modeling, intelligent tutoring systems (ITSs), etc. There are different approaches to tackle with SMF rooted in linear algebra and probability theory. In this project, given an incomplete binary matrix of students’ performances over a set of questions, estimating the probability of success or fail over unanswered questions is of interest. This problem is formulated using Maximum Likelihood Estimation (MLE) which leads to a biconvex optimization problem (this formulation is based on SPARFA [4]). The resulting optimization problem is a hard problem to deal with due to the existence of many local minima. On the other hand, when the size of the matrix of students’ performances increase, the existing algorithms are not successful; therefore, an efficient algorithm is required to solve this problem for large matrices. In this project, a parallel algorithm (i.e., a parallel version of SPARFA) is developed to solve the biconvex optimization problem and tested via a number of generated matrices. Keywords: parallel non-convex optimization, matrix factorization, sparse factor analysis 1 Introduction Educational systems have witnessed a substantial transition from traditional educational methods mainly using text books, lectures, etc. to newly developed systems which are artificial intelligent- based systems and personally tailored to the learners [4]. Personalized Learning Systems (PLSs) and Intelligent Tutoring Systems (ITSs) are two more well-known instances of such recently developed educational systems. PLSs take into account learners’ individual characteristics then customize the learning experience to the learners’ current situation and needs [2]. As computerized learning environments, ITSs model and track student learning states [1, 6, 7]. Latent Factor Model and Bayesian Knowledge Tracing are main classes in ITSs [3]. These new approaches encompass computational models from different disciplines including cognitive and learning sciences, education, 1 computational linguistics, artificial intelligence, operations research, and other fields. More details can be found in [1, 4–6]. Recently, [4] developed a new machine learning-based model for learning analytics, which approximate a students knowledge of the concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and those concepts. This model calculates the probability that a learner provides the correct response to a question in terms of three factors: their understanding of a set of underlying concepts, the concepts involved in each question, and each questions intrinsic difficulty [4]. They proposed a bi-convex maximum-likelihood-based solution to the resulting SPARse Factor Analysis (SPARFA) problem. However, the scalability of SPARFA when the number of questions and students significantly increase has not been studied yet.
sandeepsoni / MHPGeneration and MLE Estimation for Multivariate Hawkes Process
SindhujaRao7 / Classical EstimatorsA Matlab program to find estimation of a vehicle using statistical methods like Minimum Variance Unbiased Estimator (MVU), Best Linear Unbiased Estimator (BLUE), Maximum Likelihood Estimator (MLE), Cramer-Rao Lower Bound (CRLB) and plot MSE
chochkov / Mle EstimationStatistical Data Analysis - MLE estimation of Lognormal and Exponential Distribution parameters in a Competing Risks Model. Simulation on R.
idiazst / SurvdrTargeted MLE with doubly robust asymptotic distribution for estimation of survival probabilities from right censored data
yuvalofek / Probability Models Stochastic ProcessesProbability Models, Detection, and ML + MMSE estimation
omarmnfy / Power Law Fit Distribution MATLABThis repository provides MATLAB implementations of plfit and plpva functions for fitting power-law distributions to empirical data using maximum likelihood estimation (MLE) and statistical goodness-of-fit tests. These tools accurately model complex systems with significant tail behaviors, common in fields like physics, biology, and economics.
ZeonSky / Python Code MCMC To Fit The Shifted Beta Geometric Customer Lifetime Value ModelTwo professors of marketing, Peter Fader and Bruce Hardie, have developed probability models for estimating customer lifetime value (LTV). In their papers and example spreadsheets, they estimate the models using maximum-likelihood estimation (MLE). In this post, I'm going to show how to use MCMC (via pymc) to estimate one of the models they've developed. Using MCMC makes it easy to quantify the uncertainty of the model parameters, and because LTV is a function of the model parameters, to pass that uncertainty through into the estimates of LTV itself. This post is primarily about implementing the model, and I'm only going to touch briefly on the strengths of the Fader/Hardie model over simpler, back-of-the-envelope formulas you'll find if you google 'calculate customer lifetime value.' But in the interest of motivating the implementation, the model is worth understanding because: by modeling the processes underlying aggregate metrics like 'churn rate' or 'repeated buying rate,' and by allowing for heterogeneity in a customer base, it provides more insight into customer behavior and in many cases, will provide less biased predictions about future behavior of customers.
