Blog Archives

Convex Regression Model

July 5, 2018
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Convex Regression Model

This morning during the lecture on nonlinear regression, I mentioned (very) briefly the case of convex regression. Since I forgot to mention the codes in R, I will publish them here. Assume that where is some convex function. Then is convex if and only if , , Hidreth (1954) proved that ifthen is unique. Let , then where. I.e....

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Game of Friendship Paradox

June 27, 2018
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Game of Friendship Paradox

In the introduction of my course next week, I will (briefly) mention networks, and I wanted to provide some illustration of the Friendship Paradox. On network of thrones (discussed in Beveridge and Shan (2016)), there is a dataset with the network of characters in Game of Thrones. The word “friend” might be abusive here, but let’s continue to call...

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Parallelizing Linear Regression or Using Multiple Sources

June 21, 2018
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Parallelizing Linear Regression or Using Multiple Sources

My previous post was explaining how mathematically it was possible to parallelize computation to estimate the parameters of a linear regression. More speficially, we have a matrix which is matrix and a -dimensional vector, and we want to compute by spliting the job. Instead of using the observations, we’ve seen that it was to possible to compute “something” using...

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Linear Regression, with Map-Reduce

June 18, 2018
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Sometimes, with big data, matrices are too big to handle, and it is possible to use tricks to numerically still do the map. Map-Reduce is one of those. With several cores, it is possible to split the problem, to map on each machine, and then to agregate it back at the end. Consider the case of the linear regression,...

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Quantile Regression (home made)

June 14, 2018
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Quantile Regression (home made)

After my series of post on classification algorithms, it’s time to get back to R codes, this time for quantile regression. Yes, I still want to get a better understanding of optimization routines, in R. Before looking at the quantile regression, let us compute the median, or the quantile, from a sample. Median Consider a sample . To compute...

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Discrete or continuous modeling ?

June 13, 2018
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Discrete or continuous modeling ?

Tuesday, we got our conference “Insurance, Actuarial Science, Data & Models” and Dylan Possamaï gave a very interesting concluding talk. In the introduction, he came back briefly on a nice discussion we usually have in economics on the kind of model we should consider. It was about optimal control. In many applications, we start with a one period economy,...

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Classification from scratch, boosting 11/8

June 8, 2018
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Classification from scratch, boosting 11/8

Eleventh post of our series on classification from scratch. Today, that should be the last one… unless I forgot something important. So today, we discuss boosting. An econometrician perspective I might start with a non-conventional introduction. But that’s actually how I understood what boosting was about. And I am quite sure it has to do with my background in...

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Classification from scratch, bagging and forests 10/8

June 8, 2018
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Classification from scratch, bagging and forests 10/8

Tenth post of our series on classification from scratch. Today, we’ll see the heuristics of the algorithm inside bagging techniques. Often, bagging is associated with trees, to generate forests. But actually, it is possible using bagging for any kind of model. Recall that bagging means “boostrap aggregation”. So, consider a model . Let denote the estimator of obtained from...

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Classification from scratch, linear discrimination 8/8

June 6, 2018
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Classification from scratch, linear discrimination 8/8

Eighth post of our series on classification from scratch. The latest one was on the SVM, and today, I want to get back on very old stuff, with here also a linear separation of the space, using Fisher’s linear discriminent analysis. Bayes (naive) classifier Consider the follwing naive classification ruleor(where is the density in the continuous case). In the...

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Classification from scratch, SVM 7/8

June 6, 2018
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Classification from scratch, SVM 7/8

Seventh post of our series on classification from scratch. The latest one was on the neural nets, and today, we will discuss SVM, support vector machines. A formal introduction Here takes values in . Our model will be Thus, the space is divided by a (linear) border The distance from point to is If the space is linearly separable,...

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