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Machine Learning

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Neural Networks

Sentiment Analysis. LSA. How to handle Imbalanced Classification Problems in machine learning? How to handle Imbalanced Classification Problems in machine learning? Spearmans. 26 Great Articles and Tutorials about Regression Analysis. Twitter. Complete guide to create a Time Series Forecast (with Codes in Python) Learn the steps to create a Time Series forecastAdditional focus on Dickey-Fuller test & ARIMA (Autoregressive, moving average) modelsLearn the concepts theoretically as well as with their implementation in python Time Series (referred as TS from now) is considered to be one of the less known skills in the data science space (Even I had little clue about it a couple of days back).

I set myself on a journey to learn the basic steps for solving a Time Series problem and here I am sharing the same with you. These will definitely help you get a decent model in any future project you take up! Complete guide to create a time series forecast with python Before going through this article, I highly recommend reading A Complete Tutorial on Time Series Modeling in R and taking the free Time Series Forecasting course. It focuses on fundamental concepts and I will focus on using these concepts in solving a problem end-to-end along with codes in Python. Our journey would go through the following steps: Lesson1. DataOrigami. 12 Algorithms Every Data Scientist Should Know.

Anomaly Detection

Deep Learning. Bayesian - Estimating the covariance posterior distribution of a multivariate gaussian. PAC. F Distribution. Machine Learning in 7 Pictures. Basic machine learning concepts of Bias vs Variance Tradeoff, Avoiding overfitting, Bayesian inference and Occam razor, Feature combination, Non-linear basis functions, and more - explained via pictures. By Deniz Yuret, Feb 2014. I find myself coming back to the same few pictures when explaining basic machine learning concepts. Below is a list I find most illuminating. 1. Bias vs Variance tradeoff - Test and training error: Why lower training error is not always a good thing: ESL Figure 2.11. 2. 3. 4. 5. 6. 7. Occam’s Razor and PAC-learning. So far our discussion of learning theory has been seeing the definition of PAC-learning, tinkering with it, and seeing simple examples of learnable concept classes.

We’ve said that our real interest is in proving big theorems about what big classes of problems can and can’t be learned. One major tool for doing this with PAC is the concept of VC-dimension, but to set the stage we’re going to prove a simpler theorem that gives a nice picture of PAC-learning when your hypothesis class is small. In short, the theorem we’ll prove says that if you have a finite set of hypotheses to work with, and you can always find a hypothesis that’s consistent with the data you’ve seen, then you can learn efficiently.

It’s obvious, but we want to quantify exactly how much data you need to ensure low error. The Chernoff bound One tool we will need in this post, which shows up all across learning theory, is the Chernoff-Hoeffding bound. Theorem: Let. . , and. . , and we’ll want to bound this by , where . ). . Is. Probably Approximately Correct — a Formal Theory of Learning. In tackling machine learning (and computer science in general) we face some deep philosophical questions. Questions like, “What does it mean to learn?” And, “Can a computer learn?” And, “How do you define simplicity?” And, “Why does Occam’s Razor work? (Why do simple hypotheses do well at modelling reality?)” In a very deep sense, learning theorists take these philosophical questions — or at least aspects of them — give them fleshy mathematical bodies, and then answer them with theorems and proofs.

These fleshy bodies might have imperfections or they might only address one small part of a big question, but the more we think about them the closer we get to robust answers and, as a reader of this blog might find relevant, useful applications. But before we jump too far ahead of ourselves, we need to get through the basics. Leslie Valiant So let’s jump right in and see what this award-winning definition is all about. Learning Intervals . ). Is in the interval, and a 0 otherwise. And . . . . All entries. Metodi Statistici per l'Apprendimento. Orario lezioni Materiale bibliografico: Il materiale sarà fornito dal docente sotto forma di dispense integrate da riferimenti bibliografici.

Per colmare eventuali lacune in calcolo delle probabilità e statistica e ottimizzazione non lineare si consiglia la consultazione dei testi seguenti: Paolo Baldi, Calcolo delle probabilità e statistica (seconda edizione). McGraw-Hill, 1998. Vincenzo Capasso e Daniela Morale, Una guida allo studio della probabilità e statistica matematica. Società editrice Esculapio, 2009. Testi generali di apprendimento automatico: Shai Shalev-Shwartz e Shai Ben-David, Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, 2014. Obiettivi L'apprendimento automatico si occupa dello sviluppo di algoritmi per la costruzione di modelli predittivi sulla base di un insieme di osservazioni relative ad un dato fenomeno.

Programma Link utili Esami L'esame consiste in un approfondimento teorico oppure un progetto pratico. Avvisi.

Causal Inference

Welcome. The Two Cultures: statistics vs. machine learning? Dictionary of Algorithms and Data Structures. How Do I Start Learning Data Analysis? As an instructor in the Data Analyst Nanodegree, I know how important it is to have a learning plan when starting something new. When I first started learning about data analysis and data science three years ago, I came across the following roadmap of skills, and I couldn’t help but feel overwhelmed. Where do I start? What programming language should I learn first? And why are the names of animals included in the list of skills (I’m looking at you Python, Pandas, and Pig)? Source: Map of Data Science Skills to Learn Credit: Swami Chandrasekaran Learning about data analysis shouldn’t feel so overwhelming and difficult to the point of discouragement.

For starters, you will want to use a programming language so that you can record your work and share it with others. Get started today! Getting started is usually the most intimidating part. One encouraging thing about R, especially when you’re getting started, is that just a few commands can lead to powerful insights. Overview of statistics.

Putting the methods you use into context It may come as a surprise, but the way you were probably taught statistics during your undergraduate years is not the way statistics is done. There are a number of different ways of thinking about and doing statistics. It might be disconcerting to learn that there is no consensus amongst statisticians about what a probability is for example (a subjective degree of belief, or an objective long-run frequency?). Typically, scientists are only exposed to the frequentist school, which has been criticised on a number of grounds (discussed briefly below), and this is an incredible shortcoming of standard science education. Not knowing the big picture about other schools of thought, methods of analysis, or ways of interpreting evidence is a serious limitation for anyone who conducts experiments and interprets the results.

Bayesian Bayesian methods are arguably the oldest; the Rev. Frequentist Information-Theoretic Likelihood Summary References Cohen J (1994). Sampling Distribution of Difference Between Means. Sampling Distribution of Difference Between Means Author(s) David M. Lane Prerequisites Sampling Distributions, Sampling Distribution of the Mean, Variance Sum Law I Learning Objectives State the mean and variance of the sampling distribution of the difference between means Compute the standard error of the difference between means Compute the probability of a difference between means being above a specified value The sampling distribution of the difference between means can be thought of as the distribution that would result if we repeated the following three steps over and over again: (1) sample n1 scores from Population 1 and n2 scores from Population 2, (2) compute the means of the two samples (M1 and M2), and (3) compute the difference between means, M1 - M2.

As you might expect, the mean of the sampling distribution of the difference between means is: which says that the mean of the distribution of differences between sample means is equal to the difference between population means. Olivier Cappé's Home Page. All entries.

Categorical Data

‎ Julia express. Julia Statistics. Generalized linear model. In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.

Intuition[edit] Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a set of observed values (predictors). This implies that a constant change in a predictor leads to a constant change in the response variable (i.e. a linear-response model). However, these assumptions are inappropriate for many types of response variables. Overview[edit] In this framework, the variance is typically a function, V, of the mean: Model components[edit] 1. 2. 3.

And , and as . Linear regression. In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. (This term should be distinguished from multivariate linear regression, where multiple correlated dependent variables are predicted,[citation needed] rather than a single scalar variable.) In linear regression, data are modeled using linear predictor functions, and unknown model parameters are estimated from the data. Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. Linear regression has many practical uses.

If the goal is prediction, or forecasting, or reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. Where Example. Ordinary least squares. Okun's law in macroeconomics states that in an economy the GDP growth should depend linearly on the changes in the unemployment rate. Here the ordinary least squares method is used to construct the regression line describing this law. In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear approximation.

The resulting estimator can be expressed by a simple formula, especially in the case of a single regressor on the right-hand side. The OLS estimator is consistent when the regressors are exogenous and there is no perfect multicollinearity, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Linear model[edit] Suppose the data consists of n observations { y i, x i }ni=1.

Assumptions[edit] Generalized least squares. Method outline[edit] In a typical linear regression model we observe data on n statistical units. The response values are placed in a vector Y = (y1, ..., yn)′, and the predictor values are placed in the design matrix X = [[xij]], where xij is the value of the jth predictor variable for the ith unit. The model assumes that the conditional mean of Y given X is a linear function of X, whereas the conditional variance of the error term given X is a known matrix Ω. This is usually written as Here β is a vector of unknown “regression coefficients” that must be estimated from the data. Suppose b is a candidate estimate for β. Since the objective is a quadratic form in b, the estimator has an explicit formula: Properties[edit] GLS is equivalent to applying ordinary least squares to a linearly transformed version of the data.

Weighted least squares[1][edit] A special case of GLS called weighted least squares (WLS) occurs when all the off-diagonal entries of Ω are 0. And estimates of the residuals so. Dummy variable (statistics) In statistics and econometrics, particularly in regression analysis, a dummy variable (also known as an indicator variable, design variable, Boolean indicator, categorical variable, binary variable, or qualitative variable[1][2]) is one that takes the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.[3][4] Dummy variables are used as devices to sort data into mutually exclusive categories (such smoker/non-smoker, etc.).[2] For example, in econometric time series analysis, dummy variables may be used to indicate the occurrence of wars or major strikes.

A dummy variable can thus be thought of as a truth value represented as a numerical value 0 or 1 (as is sometimes done in computer programming). Dummy variables are "proxy" variables or numeric stand-ins for qualitative facts in a regression model. Figure 1 : Graph showing wage = α0 + δ0female + α1education + U, δ0 < 0. Wage = α0 + δ0female + α1education + U where where, Machine Learning | Electrical Engineering and Computer Science. The Gaussian Processes Web Site.