Valerio Gherardi | R-bloggers

AIC in the well-specified linear model: theory and simulation

May 16, 2024 | Valerio Gherardi

Theory AIC Consider the AIC for the usual linear model : where is the dimension of the covariate vector and is the ML estimate of the conditional variance. The expectation of Equation 1 under model assumptions can be found by using t...

$Y = X\beta + \varepsilon$

[Read more...]

AIC in the well-specified linear model: theory and simulation

May 16, 2024 | Valerio Gherardi

Theory AIC Consider the AIC for the usual linear model : where is the dimension of the covariate vector and is the ML estimate of the conditional variance. The expectation of Equation 1 under model assumptions can be found by using t...

$Y = X\beta + \varepsilon$

[Read more...]

AIC in the well-specified linear model: theory and simulation

May 15, 2024 | Valerio Gherardi

Theory AIC Consider the AIC for the usual linear model $Y = X\beta + \varepsilon$: \[ \text{AIC} = \frac{1}{2}\ln(2\pi e\hat \sigma^2)+\frac{p+1}{N} (\#eq:AIC) \] where $p$ is the dimension of the covariate vector $X$ and $\hat \sigma ^2$ is...

[Read more...]

Grammar as a biometric for Authorship Verification

April 24, 2024 | Valerio Gherardi

About a month ago we finally managed to drop (Nini et al. 2024), “Authorship Verification based on the Likelihood Ratio of Grammar Models”, on the arXiv. Delving into topics such as authorship verification, grammar and forensics, was quite a det...

$k$

[Read more...]

Grammar as a biometric for Authorship Verification

April 24, 2024 | Valerio Gherardi

About a month ago we finally managed to drop (Nini et al. 2024), “Authorship Verification based on the Likelihood Ratio of Grammar Models”, on the arXiv. Delving into topics such as authorship verification, grammar and forensics, was quite a det...

$k$

[Read more...]

Grammar as a biometric for Authorship Verification

April 23, 2024 | Valerio Gherardi

About a month ago we finally managed to drop (Nini et al. 2024), “Authorship Verification based on the Likelihood Ratio of Grammar Models”, on the arXiv. Delving into topics such as authorship verification, grammar and forensics, was quite a detour for me, and I’d like to summarize here some of ... [Read more...]

Interpreting the Likelihood Ratio cost

November 14, 2023 | Valerio Gherardi

Intro During the last few months, I’ve been working on a machine learning algorithm with applications in Forensic Science, a.k.a. Criminalistics. In this field, one common task for the data analyst is to present the trier-of-fact (the person or...

$\Lambda(X) \equiv \frac{\text{Pr}(X\vert Y = 1)}{\text{Pr}(X\vert Y = 0)}$

[Read more...]

Interpreting the Likelihood Ratio cost

November 14, 2023 | Valerio Gherardi

Intro During the last few months, I’ve been working on a machine learning algorithm with applications in Forensic Science, a.k.a. Criminalistics. In this field, one common task for the data analyst is to present the trier-of-fact (the person or...

$\Lambda(X) \equiv \frac{\text{Pr}(X\vert Y = 1)}{\text{Pr}(X\vert Y = 0)}$

[Read more...]

AB tests and repeated checks

July 26, 2023 | Valerio Gherardi

Intro “How is the experiment going?” Also: “Do we already see something?” And my favorite one: “Did we already hit significance, or do we need more data?” If you have dealt with experiments with relatively high outcome expectations, you w...

$p$

[Read more...]

AB tests and repeated checks

July 26, 2023 | Valerio Gherardi

Intro “How is the experiment going?” Also: “Do we already see something?” And my favorite one: “Did we already hit significance, or do we need more data?” If you have dealt with experiments with relatively high outcome expectations, you w...

$p$

[Read more...]

Testing functional specification in linear regression

July 10, 2023 | Valerio Gherardi

Another one from the series on “misspecified regression models” (started with Model Misspecification and Linear Sandwiches). Intro Lately I’ve been messing around with the {lmtest} R package, a nice collection of hypothesis tests for classical ...

$X$

[Read more...]

Testing functional specification in linear regression

July 10, 2023 | Valerio Gherardi

Another one from the series on “misspecified regression models” (started with Model Misspecification and Linear Sandwiches). Intro Lately I’ve been messing around with the {lmtest} R package, a nice collection of hypothesis tests for classical ...

$X$

[Read more...]

Linear regression with autocorrelated noise

May 24, 2023 | Valerio Gherardi

Consider two time series and such that: where is noise: By iteration of Equation 2, we see that has gaussian unconditional distribution: so that individual observations of are distributed according to a perfectly specified linear m...

$X_t$

[Read more...]

Linear regression with autocorrelated noise

May 24, 2023 | Valerio Gherardi

Consider two time series and such that: where is noise: By iteration of Equation 2, we see that has gaussian unconditional distribution: so that individual observations of are distributed according to a perfectly specified linear m...

$X_t$

[Read more...]

Model Misspecification and Linear Sandwiches

May 13, 2023 | Valerio Gherardi

Introduction Traditional linear models, such as the output of the R function lm(), are often loaded with a set of strong assumptions. Take univariate regression: This equation assumes that: The conditional mean , a linear function of . The co...

$Y = q+mX+\varepsilon. \tag{1}$

[Read more...]

Model Misspecification and Linear Sandwiches

May 13, 2023 | Valerio Gherardi

Introduction Traditional linear models, such as the output of the R function lm(), are often loaded with a set of strong assumptions. Take univariate regression: This equation assumes that: The conditional mean , a linear function of . The co...

$Y = q+mX+\varepsilon. \tag{1}$

[Read more...]

An introduction to k-gram language models in R

March 8, 2021 | Valerio Gherardi

Are you interested in guest posting? Publish at DataScience+ via your RStudio editor. Category Advanced Modeling Tags Machine Learning Natural Language Processing NLP R Programming Text Mining This post offers a brief introduction to $k$-gram language models, using the R package kgrams, which provides an interface for training, evaluating ... [Read more...]

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Articles by Valerio Gherardi

AIC in the well-specified linear model: theory and simulation

AIC in the well-specified linear model: theory and simulation

AIC in the well-specified linear model: theory and simulation

Grammar as a biometric for Authorship Verification

Grammar as a biometric for Authorship Verification

Grammar as a biometric for Authorship Verification

Interpreting the Likelihood Ratio cost

Interpreting the Likelihood Ratio cost

AB tests and repeated checks

AB tests and repeated checks

Testing functional specification in linear regression

Testing functional specification in linear regression

Linear regression with autocorrelated noise

Linear regression with autocorrelated noise

Model Misspecification and Linear Sandwiches

Model Misspecification and Linear Sandwiches

An introduction to k-gram language models in R

Articles by Valerio Gherardi

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