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slides/static/img/y_fx.png diff --git a/README.md b/README.md index 003dc00..9507e09 100644 --- a/README.md +++ b/README.md @@ -25,13 +25,20 @@ Fora do horário de aula ou monitoria: ## Slides -| Slide | -|:------| +| Slide | +|:------------------------------------------------------------------------------------------------------------| +| [00-intro-curso.html](https://curso-r.github.io/202405-intro-ml/slides/00-intro-curso.html) | +| [01-intro-ml.html](https://curso-r.github.io/202405-intro-ml/slides/01-intro-ml.html) | +| [02-intro-classificacao.html](https://curso-r.github.io/202405-intro-ml/slides/02-intro-classificacao.html) | +| [03-modelos-de-arvores.html](https://curso-r.github.io/202405-intro-ml/slides/03-modelos-de-arvores.html) | ## Scripts utilizados em aula -| Exemplo | -|:--------| +| Exemplo | +|:--------------------------------------------------------------------------------------------------------------------------------| +| [01-tidymodels.R](https://curso-r.github.io/202405-intro-ml/exemplos_de_aula/01-tidymodels.R) | +| [02-tidymodels_apenas_aplicacao.R](https://curso-r.github.io/202405-intro-ml/exemplos_de_aula/02-tidymodels_apenas_aplicacao.R) | +| [modelo_ajustado.rds](https://curso-r.github.io/202405-intro-ml/exemplos_de_aula/modelo_ajustado.rds) | ## Práticas diff --git a/slides/.gitignore b/slides/.gitignore new file mode 100644 index 0000000..e43b0f9 --- /dev/null +++ b/slides/.gitignore @@ -0,0 +1 @@ +.DS_Store diff --git a/slides/00-intro-curso.Rmd b/slides/00-intro-curso.Rmd new file mode 100644 index 0000000..39be4de --- /dev/null +++ b/slides/00-intro-curso.Rmd @@ -0,0 +1,184 @@ +--- +title: "Introdução ao Machine Learning com R" +subtitle: "Introdução ao curso" +author: "" +date: "`r paste(lubridate::month(Sys.Date(), label = TRUE, abbr = FALSE), 'de', lubridate::year(Sys.Date()))`" +output: + xaringan::moon_reader: + css: ["default", "default-fonts", "static/css/custom-intro.css"] + lib_dir: libs + nature: + highlightStyle: github + highlightLines: true + countIncrementalSlides: false + ratio: "4:3" +knit: pagedown::chrome_print +--- + +```{r setup, include=FALSE} +options(htmltools.dir.version = FALSE) +``` + +class: middle, center + +# Sobre a Curso-R + +--- + +## Curso-R + + + +--- + +## Linha do tempo + +
+ +
+ +--- +## Nossos cursos + +.pull-left[ +
+ +
+ +
+ +
+ +
+] + + +.pull-right[ +
+
+

Extração de dados

+
+

Web scraping I

+

Web scraping II

+
+
+ +
+ +
+
+

Comunicação e automação

+
+

Dashboards com R

+

Deploy

+
+
+] + +--- +class: middle, center + +# Sobre o curso + +--- +## Dinâmica curso + +- As aulas serão (quase totalmente) expositivas. + +- Teremos diversos exercícios para serem feitos "em casa". + +- Os exercícios não serão avaliações, portanto não terão prazo nem nota. O objetivo deles será gerar dúvidas em vocês, para que os professores possam melhor orientá-las(los) durante o curso. + +- O certificado será emitido mediante uma **entrega final** (Kaggle InClass). O prazo da entrega final será de 30 dias após o fim do curso. + +--- + +# Programa do curso + +.pull-left[ + +### Capítulo 1 + +- Introdução ao Machine Learning +- Tidymodels +- Regressão linear, Regularização +- Overfitting +- Validação cruzada e estratégias + +### Capítulo 2 + +- Regressão logística, regressão vs classificação +- Data prep +- Métricas de performance para classificação: ROC, Acurácia + +] + +.pull-right[ +### Capítulo 3 + +- Árvores de Decisão +- Random Forest +- Boosting - XGBoost + +### Capítulo 4 + +- Data prep parte II: Matriz X +- Estudo de Caso + +] +--- + +# Não falaremos... + +- Deploy em produção + +- Redes Neurais/Deep Learning + +- Séries Temporais + +- Provas de Teoremas + +- Shiny + +--- +# Tirando dúvidas + + - **Sintam-se a vontade em fazer perguntas durante a exposição ao vivo.**. + + - Fora do horário de aula ou monitoria: + - perguntas gerais sobre o curso deverão ser feitas no Classroom. + + - perguntas sobre R, principalmente as que envolverem código, deverão ser enviadas no [nosso discourse](https://discourse.curso-r.com/). + +--- +# Por que usar o discourse? + +- Muito melhor para escrever textos que possuem códigos. Com ele, podemos usar o pacote `{reprex}`! + +- Saber pesquisar sobre erros e fazer a pergunta certa é essencial para aprender e resolver problemas de programação. + +- No discourse, teremos mais pessoas acompanhando e respondendo as dúvidas. + +- Em um ambiente aberto, as suas dúvidas vão contribuir com a comunidade. + +### https://discourse.curso-r.com/ + +--- + +## Extras + +- Teremos monitoria uma veze por semana, sempre 30 minutos antes do início das aulas (terças, das 18h30 às 19h), durante as 8 semanas de curso. + +- A gravação das aulas ficará disponível no Google Classroom por 1 ano após o final do curso. diff --git a/slides/00-intro-curso.html b/slides/00-intro-curso.html new file mode 100644 index 0000000..19e221e --- /dev/null +++ b/slides/00-intro-curso.html @@ -0,0 +1,333 @@ + + + + Introdução ao Machine Learning com R + + + + + + + + + + + + + + + + + + diff --git a/slides/00-intro-curso.pdf b/slides/00-intro-curso.pdf new file mode 100644 index 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+ + +] + +.pull-right[ + + + +] + + +--- + +# Referências + +.pull-left[ + + + +] + +.pull-right[ + + + +] + + +--- + +# Referências + +- [Feature Engineering and Selection: A Practical Approach for Predictive Models](http://www.feat.engineering/) + +- [Aprendizado De Máquina](http://www.rizbicki.ufscar.br/AME.pdf) + +- [Forecasting: Principles and Practice](https://otexts.com/fpp3/) + +--- + +class: middle, center, inverse + +# Introdução + +--- + +# O que é Machine Learning? + +
+ + +- Termo criado por Arthur Samuel, em 1959 + + + + +- Modelagem preditiva é um framework de análise de dados que visa gerar a estimativa mais precisa possível para uma quantidade ou fenômeno (Max Kuhn, 2014). + + +--- + +## Exemplos + +.pull-left[ + +- Previsão de churn + +- Previsão de inadimplência + +- Previsão de demanda + +- Previsão de preço + +- Previsão meteorológica + +- Diagnóstico em imagem médica + +- Carro autônomo + +- Projeção da taxa de desemprego + +] + +.pull-right[ + +- Teste A/B + +- Teste clínico + +- Eficácia de vacinas + +- Impactos de políticas públicas + +- Impactos de campanha publicitária + +- Curvas epidemiológicas + +- Projeção do PIB + +- ... + +] + + + +--- + + + +.footnote[ + fonte: [business2community](https://www.business2community.com/trends-news/10-companies-using-machine-learning-cool-ways-01889944) +] + +--- + +# Motivação + +```{r echo=FALSE, include=FALSE} +knitr::opts_chunk$set( + echo = FALSE, + message = FALSE, + warning = FALSE, + fig.width=6, + fig.height=6, + fig.align='center' +) +library(rpart) +adv <- read_csv("static/data/Advertising.csv") %>% + rename(vendas = sales) +``` + +Somos consultores e fomos contratados para dar conselhos para uma empresa aumentar as suas vendas. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +adv_ok <- adv %>% + gather(midia, investimento, -vendas) + +adv_ok %>% + ggplot(aes(x = investimento, y = vendas)) + + geom_point() + + facet_wrap(~midia, scales = "free") +``` + +* PERGUNTA: Quantas vendas terão se eu investir X? Em qual mídia eu escolho alocar meu orçamento? + +--- + +# Motivação + + +Somos consultores e fomos contratados para dar conselhos para uma empresa aumentar as suas vendas. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +adv_ok %>% + ggplot(aes(x = investimento, y = vendas)) + + geom_point() + + geom_smooth(se = FALSE) + + facet_wrap(~midia, scales = "free") +``` + +* PERGUNTA: Quantas vendas terão se eu investir X? Em qual mídia eu escolho alocar meu orçamento? + + +--- + +# Motivação - outro exemplo + + +Somos da área de inadimplência e precisamos agir para assessorar clientes em situação iminente de atraso. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +set.seed(1) +inadimplencia <- tibble::tibble( + tipo_de_contrato = rep(c("revol", "padrao", "price"), each = 1000), + valor_da_parcela = round(runif(3000, min = 500, max = 3000), digits = 0), + atrasou = rbinom(3000, 1, prob = 1/(1 + exp(-1*( + -9 + + 1.5 * (tipo_de_contrato == "revol") + + -1.5 * (tipo_de_contrato == "padrao") + + 0.005 * (valor_da_parcela) + + 1 * (valor_da_parcela > 1500) + )))) +) + +inad_curva <- inadimplencia %>% + ggplot(aes(x = valor_da_parcela, y = atrasou)) + + facet_wrap(~tipo_de_contrato, scales = "free") + + xlim(c(400, 3100)) + +inad_curva + + geom_point() +``` + +* PERGUNTA: Qual a probabilidade do contrato 123 atrasar a próxima fatura no mês que vem? + +--- + +# Motivação - outro exemplo + + +Somos da área de inadimplência e precisamos agir para assessorar clientes em situação iminente de atraso. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +inad_curva + + geom_point() + + geom_smooth(se = FALSE, method = "glm", method.args = list(family = "binomial")) +``` + +* PERGUNTA: Qual a probabilidade do contrato 123 atrasar a próxima fatura no mês que vem? + +--- + +# Motivação - outro exemplo + + +Somos da área de inadimplência e precisamos agir para assessorar clientes em situação iminente de atraso. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +inad_curva + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 7, geom = "bar", fill = "royalblue", fun = function(x) 1) + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 7, geom = "bar", fill = "red") + + stat_summary_bin(size = 2, alpha = 1, colour = "purple", bins = 7, geom = "point") + + geom_point() + + geom_smooth(se = FALSE, method = "glm", method.args = list(family = "binomial")) +``` + +* PERGUNTA: Qual a probabilidade do contrato 123 atrasar a próxima fatura no mês que vem? + +--- + +# Motivação - outro exemplo + + +Somos da área de inadimplência e precisamos agir para assessorar clientes em situação iminente de atraso. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +inad_curva + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 12, geom = "bar", fill = "royalblue", fun = function(x) 1) + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 12, geom = "bar", fill = "red") + + stat_summary_bin(size = 2, alpha = 1, colour = "purple", bins = 12, geom = "point")+ + geom_point() + + geom_smooth(se = FALSE, method = "glm", method.args = list(family = "binomial")) +``` + +* PERGUNTA: Qual a probabilidade do contrato 123 atrasar a próxima fatura no mês que vem? + + +--- + +# Motivação - outro exemplo + + +Somos da área de inadimplência e precisamos agir para assessorar clientes em situação iminente de atraso. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +inad_curva + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 100, geom = "bar", fill = "royalblue", fun = function(x) 1) + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 100, geom = "bar", fill = "red") + + stat_summary_bin(size = 2, alpha = 1, colour = "purple", bins = 100, geom = "point")+ + geom_point() + + geom_smooth(se = FALSE, method = "glm", method.args = list(family = "binomial")) +``` + +* PERGUNTA: Qual a probabilidade do contrato 123 atrasar a próxima fatura no mês que vem? + +--- + +# Motivação - outro exemplo + + +Somos da área de inadimplência e precisamos agir para assessorar clientes em situação iminente de atraso. + +Obtivemos o seguinte banco de dados + +```{r, fig.width = 10, fig.height = 4} +inad_curva + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 1000, geom = "bar", fill = "royalblue", fun = function(x) 1) + + stat_summary_bin(size = 1, alpha = 0.1, colour = "white", bins = 1000, geom = "bar", fill = "red") + + stat_summary_bin(size = 2, alpha = 1, colour = "purple", bins = 1000, geom = "point")+ + geom_point() + + geom_smooth(se = FALSE, method = "glm", method.args = list(family = "binomial")) +``` + +* PERGUNTA: Qual a probabilidade do contrato 123 atrasar a próxima fatura no mês que vem? + + +--- + +# Machine Learning + +Matematicamente, queremos encontrar uma função $f()$ tal que: + + + +
+
+
+
+
+
+
+ +Nos exemplos: + +$vendas = f(midia, investimento)$ + +$inadimplência = f(valor da parcela, tipo de contrato)$ + + + +--- + +# Modo - Regressão e Classificação + +Existem dois principais tipos de problemas em Machine Learning: + +.pull-left[ + +## Regressão + +__Y__ é uma variável contínua. + +- Volume de vendas +- Peso +- Temperatura +- Valor de Ações + +] + +.pull-right[ + +## Classificação + +__Y__ é uma variável categórica. + +- Fraude/Não Fraude +- Pegou em dia/Não pagou +- Cancelou assinatura/Não cancelou +- Gato/Cachorro/Cavalo/Outro + +] + + +--- + +# Exemplos de f(x) + +```{r, fig.width = 12, fig.height = 5} +adv_ok <- adv %>% + gather(midia, investimento, -vendas) + +arvore <- rpart::rpart(vendas ~ investimento + midia, data = adv_ok) +regressao_linear <- lm(vendas ~ investimento + midia, data = adv_ok) +adv_ok <- adv_ok %>% + mutate( + arvore = predict(arvore, newdata = .), + regressao_linear = predict(regressao_linear, newdata = .), + ) +grafico_sem_curva <- adv_ok %>% + ggplot(aes(x = investimento, y = vendas)) + + geom_point() + + facet_wrap(~midia, scales = "free") + + labs(colour = "f(x):") + + theme(legend.position = "bottom", + legend.text = element_text(size = 22), + legend.title = element_text(size = 30)) + +grafico_curva_arvore <- grafico_sem_curva + + geom_line(aes(y = arvore, colour = "Árvore de Decisão"), size = 2) +``` + +```{r, fig.width = 12, fig.height = 5} +grafico_curva_regressao_linear <- grafico_sem_curva + + geom_step(aes(y = regressao_linear, colour = "Regressão Linear"), size = 2) +grafico_curva_regressao_linear +``` + +--- + +# Exemplos de f(x) + +```{r, fig.width = 12, fig.height = 5} +grafico_curva_arvore +``` + + + +--- + +# Exemplos de f(x) + +```{r, fig.width = 12, fig.height = 5} +arvore_inad <- rpart::rpart(atrasou ~ valor_da_parcela + tipo_de_contrato, control = rpart::rpart.control(cp = 0.005), data = inadimplencia) +regressao_linear_inad <- glm(atrasou ~ valor_da_parcela * tipo_de_contrato, data = inadimplencia, family = "binomial") +inadimplencia <- inadimplencia %>% + dplyr::mutate( + arvore = predict(arvore_inad, newdata = .), + regressao_logistica = predict(regressao_linear_inad, newdata = ., type = "response"), + ) +grafico_sem_curva_inad <- inadimplencia %>% + ggplot(aes(x = valor_da_parcela, y = atrasou)) + + geom_point() + + facet_wrap(~tipo_de_contrato, scales = "free") + + labs(colour = "f(x):") + + theme(legend.position = "bottom", + legend.text = element_text(size = 22), + legend.title = element_text(size = 30)) + +grafico_curva_arvore_inad <- grafico_sem_curva_inad + + geom_line(aes(y = arvore, colour = "Árvore de Decisão"), size = 2) +``` + +```{r, fig.width = 12, fig.height = 5} +grafico_curva_regressao_linear_inad <- grafico_sem_curva_inad + + geom_step(aes(y = regressao_logistica, colour = "Regressão Logística"), size = 2) +grafico_curva_regressao_linear_inad +``` + +--- + +# Exemplos de f(x) + +```{r, fig.width = 12, fig.height = 5} +grafico_curva_arvore_inad +``` + + + + + +--- + +# Definições e Nomenclaturas + +### A tabela por trás (do excel, do sql, etc.) + +```{r} +set.seed(1) +adv_ok %>% + sample_n(8) %>% + mutate_if(is.numeric, round, digits = 1) %>% + select(midia, investimento, vendas) %>% + kable(format = "html") +``` + + +--- + +# Definições e Nomenclaturas + +* $X_1$, $X_2$, ..., $X_p$: variáveis explicativas (ou variáveis independentes ou *features* ou preditores). + +- $\boldsymbol{X} = {X_1, X_2, \dots, X_p}$: conjunto de todas as *features*. + +* __Y__: variável resposta (ou variável dependente ou *target*). +* __Ŷ__: valor **esperado** (ou predição ou estimado ou *fitted*). +* $f(X)$ também é conhecida também como "Modelo" ou "Hipótese". + +## No exemplo: + +- $X_1$: `midia` - indicadador de se a propaganda é para jornal, rádio, ou TV. +- $X_2$: `investimento` - valor do orçamento + +* __Y__: `vendas` - qtd vendida + + +--- + +# Definições e Nomenclaturas + +### **Observado** *versus* **Esperado** + +- __Y__ é um valor **observado** (ou verdade ou *truth*) +- __Ŷ__ é um valor **esperado** (ou predição ou estimado ou *fitted*). +- __Y__ - __Ŷ__ é o resíduo (ou erro) + +Por definição, $\hat{Y} = f(x)$ que é o valor que a função $f$ retorna. + +```{r, fig.width = 15, fig.height = 4, out.width=750} +ponto_predito = tibble::tribble( + ~investimento, ~yend, ~midia, + 150, 0, "TV", + 35, 0, "radio", + 60, 0, "newspaper" +) %>% + mutate( + vendas = predict(arvore, .) + ) +seta_first <- arrow(ends = "first", type = "closed", angle = 20, length = unit(20, "pt")) +seta_last <- arrow(ends = "last", type = "closed", angle = 20, length = unit(20, "pt")) +grafico_curva_arvore + + geom_segment(aes(xend = investimento, yend = yend), arrow = seta_first, data = ponto_predito, colour = "purple", size = 1, linetype = "dashed") + + geom_segment(aes(xend = 0, yend = vendas), arrow =seta_last, data = ponto_predito, colour = "purple", size = 1, linetype = "dashed") + + geom_point(data = ponto_predito, colour = "purple", size = 5) + + theme_minimal(20) + + theme(legend.position = "left", + legend.text = element_text(size = 22), + legend.title = element_text(size = 30)) +``` + + +--- + +# Definições e Nomenclaturas + +### **Observado** *versus* **Esperado** + +- __Y__ é um valor **observado** (ou verdade ou *truth*) +- __Ŷ__ é um valor **esperado** (ou predição ou estimado ou *fitted*). +- __Y__ - __Ŷ__ é o resíduo (ou erro) + +Por definição, $\hat{Y} = f(x)$ que é o valor que a função $f$ retorna. + +```{r, fig.width = 15, fig.height = 4, out.width=750} +ponto_predito = tibble::tribble( + ~investimento, ~yend, ~midia, + 150, 0, "TV", + 35, 0, "radio", + 60, 0, "newspaper" +) %>% + mutate( + vendas = predict(regressao_linear, .) + ) + +grafico_curva_regressao_linear + + geom_segment(aes(xend = investimento, yend = yend), arrow = seta_first, data = ponto_predito, colour = "purple", size = 1, linetype = "dashed") + + geom_segment(aes(xend = 0, yend = vendas), arrow = seta_last, data = ponto_predito, colour = "purple", size = 1, linetype = "dashed") + + geom_point(data = ponto_predito, colour = "purple", size = 5) + + theme_minimal(20) + + theme(legend.position = "left", + legend.text = element_text(size = 22), + legend.title = element_text(size = 30)) +``` + + +--- + +# Definições e Nomenclaturas + +### A tabela por trás depois das predições + +```{r} +library(kableExtra) +set.seed(1) +adv_ok %>% + sample_n(8) %>% + mutate_if(is.numeric, round, digits = 1) %>% + select(midia, investimento, everything()) %>% + kable(format = "html") %>% + column_spec(4:5, color = "purple", bold = TRUE) +``` + + + + + +--- + +# Outro Exemplo: Classificação + +### A tabela por trás (do excel, do sql, etc.) + +```{r} +set.seed(1) +inadimplencia %>% + dplyr::sample_n(8) %>% + dplyr::mutate_if(is.numeric, round, digits = 1) %>% + dplyr::select(tipo_de_contrato, valor_da_parcela, atrasou) %>% + kable(format = "html") +``` + + +--- + +# Outro Exemplo: Classificação + +* $X_1$, $X_2$, ..., $X_p$: variáveis explicativas (ou variáveis independentes ou *features* ou preditores). + +- $\boldsymbol{X} = {X_1, X_2, \dots, X_p}$: conjunto de todas as *features*. + +* __Y__: variável resposta (ou variável dependente ou *target*). +* __Ŷ__: valor **esperado** (ou predição ou score ou *fitted*). +* $f(X)$ também é conhecida também como "Modelo" ou "Hipótese". + +## No exemplo: + +- $X_1$: `tipo_de_contrato` - flags de se o contrato é padrao, price, ou revol. +- $X_2$: `valor_da_parcela` - Valor da parcela do financiamento. + +* __Y__: `atrasou` - indicador de atraso maior que 30 dias na parcela. + + +--- + +# Outro Exemplo: Classificação + +### **Observado** *versus* **Esperado** + +- __Y__ é um valor **observado** (ou rótulo ou target ou verdade ou *truth*) +- __Ŷ__ é um valor **esperado** (ou score ou probabilidade predita). +- __log(Ŷ)__ ou __log(1-Ŷ)__ é o resíduo (ou erro) + +Por definição, $\hat{Y} = f(x)$ que é o valor que a função $f$ retorna. + +```{r, fig.width = 15, fig.height = 4, out.width=750} +ponto_predito_inad = tibble::tribble( + ~valor_da_parcela, ~yend, ~tipo_de_contrato, + 1800, 0, "padrao", + 1800, 0, "revol", + 1800, 0, "price" +) %>% + dplyr::mutate( + atrasou = predict(arvore_inad, .) + ) + +grafico_curva_arvore_inad + + geom_segment(aes(xend = valor_da_parcela, yend = yend), arrow = seta_first, data = ponto_predito_inad, colour = "purple", size = 1, linetype = "dashed") + + geom_segment(aes(xend = 0, yend = atrasou), arrow = seta_last, data = ponto_predito_inad, colour = "purple", size = 1, linetype = "dashed") + + geom_point(data = ponto_predito_inad, colour = "purple", size = 5) + + theme_minimal(20) + + theme(legend.position = "left", + legend.text = element_text(size = 22), + legend.title = element_text(size = 30)) +``` + + +--- + +# Outro Exemplo: Classificação + +### **Observado** *versus* **Esperado** + +- __Y__ é um valor **observado** (ou rótulo ou target ou verdade ou *truth*) +- __Ŷ__ é um valor **esperado** (ou score ou probabilidade predita). +- __log(Ŷ)__ ou __log(1-Ŷ)__ é o resíduo (ou erro) + +Por definição, $\hat{Y} = f(x)$ que é o valor que a função $f$ retorna. + +```{r, fig.width = 15, fig.height = 4, out.width=750} +ponto_predito_inad = tibble::tribble( + ~valor_da_parcela, ~yend, ~tipo_de_contrato, + 1800, 0, "padrao", + 1800, 0, "revol", + 1800, 0, "price" +) %>% + dplyr::mutate( + atrasou = predict(regressao_linear_inad, ., type = "response") + ) + +grafico_curva_regressao_linear_inad + + geom_segment(aes(xend = valor_da_parcela, yend = yend), arrow = seta_first, data = ponto_predito_inad, colour = "purple", size = 1, linetype = "dashed") + + geom_segment(aes(xend = 0, yend = atrasou), arrow = seta_last, data = ponto_predito_inad, colour = "purple", size = 1, linetype = "dashed") + + geom_point(data = ponto_predito_inad, colour = "purple", size = 5) + + theme_minimal(20) + + theme(legend.position = "left", + legend.text = element_text(size = 22), + legend.title = element_text(size = 30)) +``` + + +--- + +# Outro Exemplo: Classificação + +### A tabela por trás depois das predições + +```{r} +set.seed(1) +inadimplencia %>% + dplyr::sample_n(8) %>% + dplyr::mutate_if(is.numeric, round, digits = 2) %>% + dplyr::select(tipo_de_contrato, valor_da_parcela, everything()) %>% + kable(format = "html") %>% + column_spec(4:5, color = "purple", bold = TRUE) +``` + + +--- + +## Desempenho vs Interpretabilidade da f(x) + +```{r} +#![](https://user-images.githubusercontent.com/4706822/47456108-01d5c880-d7aa-11e8-899a-74804f74afc5.png) +``` + +```{r, fig.width=11, fig.height=7, out.width=600} +library(ggrepel) +set.seed(1) +tribble( + ~modelo, ~`Desempenho`, ~Interpretabilidade, + "Regressão Linear", 0, 3, + "Regressão Logística", 0, 3, + "Árvore de Decisão", 1, 2.2, + "Generalized Additive Models", 1.5, 1.5, + "Redes Neurais, Deep Learning", 3, 1, + "Bagging, Boosting", 3.2, 0.8, + "SVM", 2.6, 0.5 +) %>% + ggplot(aes(x = `Desempenho`, y = Interpretabilidade)) + + geom_text_repel(aes(label = modelo), size = 7) + + theme_minimal(24) + + scale_x_continuous(breaks = c(0, 3.2), labels = c("Baixo", "Alto")) + + scale_y_continuous(breaks = c(0, 3.5), labels = c("Baixo", "Alto")) + +``` + +Características importantes: interprabilidade, custo computacional e poder preditivo. + +--- + +# Por que ajustar uma f? + +* Predição +* Inferência + +## Predição + +Em muitas situações X está disponível facilmente mas, Y não é fácil de descobrir. (Ou mesmo não é possível descobrí-lo). Queremos que $\hat{Y} = \hat{f}(X)$ seja uma boa estimativa (preveja bem o futuro). +Neste caso não estamos interessados em como é a estrutura $\hat{f}$ desde que ela apresente predições boas para $Y$. + +Por exemplo: + +* Meu cliente vai atrasar a fatura no mês que vem? + +--- + +# Por que ajustar uma f? + +* Predição +* Inferência + +## Inferência + +Em inferência estamos mais interessados em entender a relação entre as variáveis explciativas $X$ e a variável resposta $Y$. + +Por exemplo: + +* A dose da droga é eficaz para o tratamento da doença X até quanto? +* **Quanto que é** o impacto nas vendas para cada real investido em TV? + + +Neste material focaremos em **predição**. + +--- + +# Por que ajustar uma f? + + + + + +--- + +## Métricas - "Melhor f(x)" segundo o quê? + +Queremos a $f(x)$ que **erre menos**. + +Exemplo de **métrica** de erro: **R**oot **M**ean **S**quared **E**rror. + +$$ +RMSE = \sqrt{\frac{1}{N}\sum(y_i - \hat{y_i})^2} +$$ + +```{r, fig.width=10, fig.height=4, warning=FALSE} +melhor_reta <- lm(dist ~ speed, data = cars) +cars_com_predicoes <- melhor_reta %>% + broom::augment() %>% + rename(pred_melhor_reta = .fitted) %>% + mutate( + pred_reta_a_mao = 50 + 3 * speed + ) + +grafico_residuos_melhor_reta <- cars_com_predicoes %>% + ggplot(aes(x = speed, y = dist)) + + geom_point(size = 2) + + geom_abline( + intercept = melhor_reta$coefficients[1], + slope = melhor_reta$coefficients[2], + size = 1, + colour = "salmon" + ) + + geom_segment(aes(xend = speed, yend = pred_melhor_reta), colour = "purple", size = 0.8) + + labs( + subtitle = "Resíduos da Melhor Reta", + title = "Os segmentos azuis são os resíduos (ou o quanto o modelo errou naqueles pontos)." + ) + +grafico_residuos_reta_a_mao <- cars_com_predicoes %>% + ggplot(aes(x = speed, y = dist)) + + geom_point(size = 2) + + geom_abline( + intercept = 50, + slope = 3, + size = 1, + colour = "orange" + ) + + geom_segment(aes(xend = speed, yend = pred_reta_a_mao), colour = "purple", size = 0.8) + + labs( + subtitle = "Resíduos da Reta Escolhida a Mão" + ) +library(patchwork) +grafico_residuos_melhor_reta + grafico_residuos_reta_a_mao +``` + + + +--- + +## Métricas - "Melhor f(x)" segundo o quê? + +Queremos a $f(x)$ que **erre menos**. + +Exemplo de métrica de erro: **R**oot **M**ean **S**quared **E**rror. + +$$ +RMSE = \sqrt{\frac{1}{N}\sum(y_i - \hat{y_i})^2} +$$ + +Ou seja, nosso **objetivo** é + +### Encontrar $f(x)$ que nos retorne o ~menor~ RMSE. + +--- + +## Métricas - "Melhor f(x)" segundo o quê? + +Queremos a reta que **erre menos**. + +Exemplo: Modelo de regressão linear $f(x) = \beta_0 + \beta_1 x$. + + + + +.footnote[ + +Fonte: [https://alykhantejani.github.io/images/gradient_descent_line_graph.gif](https://alykhantejani.github.io/images/gradient_descent_line_graph.gif) + +] + + + +--- + +## Métricas - "Melhor f(x)" segundo o quê? + +Queremos a $f(x)$ que **erre menos**. + +Exemplo de métrica de erro: **R**oot **M**ean **S**quared **E**rror. + +$$ +RMSE = \sqrt{\frac{1}{N}\sum(y_i - \hat{y_i})^2} +$$ + + +.pull-left[ + +MAE: Mean Absolute Error + +$$ +MAE = \frac{1}{N}\sum|y_i - \hat{y_i}| +$$ + +] + +.pull-right[ + +R2: R-squared + +$$ +R^2 = 1 - \frac{\sum(y_i - \color{salmon}{\hat{y_i}})^2}{\sum(y_i - \color{royalblue}{\bar{y}})^2} +$$ +] + +--- + +## Métricas - "Melhor f(x)" segundo o quê? + +Na classificação a estratégia é a mesma. Queremos a curva que **erre menos**. + +Exemplo: Modelo de regressão logística $f(x) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x)}}$. + +.pull-left[ + + + +] + +.pull-right[ + +Métrica de Erro da Logística: + +$$D = \frac{-1}{N}\sum[y_i \log\hat{y_i} + (1 - y_i )\log(1 - \hat{y_i})]$$ +Em que + +$$\hat{y}_i = f(x_i) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x_i)}}$$ + +] + +--- + +# Métricas + +Métricas: para medir o quanto a $f(x)$ está errando as previsões. + +.pull-left[ + +## Regressão + +__Y__ é uma variável contínua. + +- **RMSE** +- R2 +- MAE +- MAPE +... +] + +.pull-right[ + +## Classificação + +__Y__ é uma variável categórica. + +- **Deviance (Cross-Entropy)** +- Acurácia +- AUROC +- Precision/Recall +- F1 +- Kappa +... +] + +[lista de métricas no `yardstick`](https://tidymodels.github.io/yardstick/articles/metric-types.html) + + + + + +--- + +# Regressão Linear + + + +.pull-left[ + +### Regressão Linear Simples + +$$ +y = \beta_0 + \beta_1x +$$ + +### Exemplo: + +$$ +dist = \beta_0 + \beta_1speed +$$ + +```{r, eval = FALSE, echo=TRUE} +### No R: +linear_reg() %>% + fit(dist ~ speed, data=cars) +``` + + +] + + +.pull-right[ + +```{r,echo = FALSE, fig.height=4.5} +grafico_da_reta <- ggplot(cars, aes(x = speed, y = dist)) + + geom_point(size = 5) + + geom_smooth(se = FALSE, size = 3, method = "lm", colour = "red") + + theme_minimal(24)+ + labs( + title = " " + ) + +grafico_da_reta +``` + +.footnote[ +Ver [ISL](https://www.ime.unicamp.br/~dias/Intoduction%20to%20Statistical%20Learning.pdf) página 61 (Simple Linear Regression). +] + + +] + + + + + + +--- + +# Regressão Linear + + +.pull-left[ + +### Regressão Linear Múltipla + +$$ +y = \beta_0 + \beta_1x_1 + \dots + \beta_px_p +$$ + +### Exemplo: + +$$ +mpg = \beta_0 + \beta_1wt + \beta_2disp +$$ + +```{r, eval = FALSE, echo=TRUE} +### No R: +linear_reg() %>% + fit(mpg ~ wt + disp, data=mtcars) +``` + +] + +.pull-right[ + +```{r, fig.height=4, fig.align="center", fig.width=7, echo=FALSE} +# x, y, z variables +x <- mtcars$wt +y <- mtcars$disp +z <- mtcars$mpg +# Compute the linear regression (z = ax + by + d) +fit <- lm(z ~ x + y) +# predict values on regular xy grid +grid.lines = 26 +x.pred <- seq(min(x), max(x), length.out = grid.lines) +y.pred <- seq(min(y), max(y), length.out = grid.lines) +xy <- expand.grid( x = x.pred, y = y.pred) +z.pred <- matrix(predict(fit, newdata = xy), + nrow = grid.lines, ncol = grid.lines) +library(plotly) +fig <- plot_ly(data = mtcars) %>% + add_trace(x = ~wt, y = ~disp, z = ~mpg, + type = "scatter3d", mode = "markers", + opacity = .8) %>% + add_trace(z = z.pred, + x = x.pred, + y = y.pred, + type = "surface", + opacity = .9) +fig +``` + +.footnote[ +Fonte: [sthda.com](http://www.sthda.com/english/wiki/impressive-package-for-3d-and-4d-graph-r-software-and-data-visualization) +] + +] + + + + + +--- + +# Regressão Linear - "Melhor Reta" + +Queremos a reta que **erre menos**. + +Uma métrica de erro: RMSE + +$$ +RMSE = \sqrt{\frac{1}{N}\sum(y_i - \hat{y_i})^2} = \sqrt{\frac{1}{N}\sum(y_i - \color{red}{(\hat{\beta}_0 + \hat{\beta}_1speed)})^2} +$$ + +Ou seja, nosso é **encontrar os $\hat{\beta}'s$ que nos retorne o ~menor~ RMSE.** + +#### IMPORTANTE! + +o RMSE é **Métrica** que a regressão usa como **Função de Custo**. + +- **Função de Custo** - **Métrica** usada para encontrar os melhores parâmetros. + +--- + + +## Qual o valor ótimo para $\beta_0$ e $\beta_1$? + +No nosso exemplo, a nossa **HIPÓTESE** é de que + +$$ +dist = \beta_0 + \beta_1speed +$$ + +Então podemos escrever o RMSE + +$$ +RMSE = \sqrt{\frac{1}{N}\sum(y_i - \hat{y_i})^2} = \sqrt{\frac{1}{N}\sum(y_i - \color{red}{(\hat{\beta}_0 + \hat{\beta}_1speed)})^2} +$$ +.pull-left[ +Método mais utilizado para otimizar modelos com parâmetros: **Gradient Descent** + +Ver [Wikipedia do Gradient Descent](https://en.wikipedia.org/wiki/Gradient_descent) + +] + +.pull-right[ + +] + + + +--- + +# Regressão Linear - "Melhor Reta" + +Queremos a reta que **erre menos**. + +Modelo: $y = \beta_0 + \beta_1 x$ + + + +.footnote[ + +Fonte: [https://alykhantejani.github.io/images/gradient_descent_line_graph.gif](https://alykhantejani.github.io/images/gradient_descent_line_graph.gif) + +] + + +--- + +## Depois de estimar... + +$$ +\hat{y} = \hat{f}(x) = \hat{\beta}_0 + \hat{\beta}_1x +$$ + +### Exemplo: + +$$ +\hat{dist} = \hat{\beta}_0 + \hat{\beta}_1speed +$$ + +Colocamos um $\hat{}$ em cima dos termos para representar "estimativas". Ou seja, $\hat{y}_i$ é uma estimativa de $y_i$. No nosso exemplo, + +- $\hat{\beta}_0$ é uma estimativa de $\beta_0$ e vale `-17.5`. +- $\hat{\beta}_1$ é uma estimativa de $\beta_1$ e vale `3.9`. +- $\hat{dist}$ é uma estimativa de $dist$ e vale `-17.5 + 3.9 x speed`. + +```{r, echo=TRUE} +# Exercício: se speed for 15 m/h, quanto que +# seria a distância dist esperada? +``` + +--- + +## Tidymodels + +- Conjunto de pacotes/framework para desenvolvimento de modelos preditivos. Muitos tutoriais e guias no [site](https://www.tidymodels.org/). + +- Em desenvolvimento ativo pela RStudio. Possui muitas semelhanças com o 'tidyverse' o que faz com que mais prático. + +- Unifica o uso dos modelos já existentes no R. Ele é também extensível: você pode implementar um novo modelo +que funcione com o tidymodels. + +- Alternativas: [{caret}](https://topepo.github.io/caret/), [{mlr3}](https://mlr3.mlr-org.com/), [{scikit-learn}](https://scikit-learn.org/stable/) (Python), [{PyCaret}](https://pycaret.org/) (Python). Em geral é fácil migrar de um framework p/ o outro - a parte mais difícil é aprender o fluxo de trabalho de **machine learning**. + +--- +class: middle, center + +## Exemplo 01 + +--- + +```{r, echo=FALSE} +library(parsnip) +library(ggplot2) +# Dados ------------------------------------------------------------------- +data("diamonds") + +set.seed(12) +diamondsinho <- diamonds %>% + filter(x > 0) %>% + sample_n(13) + +# definicao do modelo ----------------------------------------------------- +especificacao_modelo1 <- linear_reg() %>% + set_engine("lm") %>% + set_mode("regression") + +especificacao_modelo2 <- linear_reg() %>% + set_engine("lm") %>% + set_mode("regression") + + +# ajuste do modelo -------------------------------------------------------- +ajuste_modelo1 <- especificacao_modelo1 %>% fit(price ~ poly(x, 2), data = diamondsinho) +ajuste_modelo2 <- especificacao_modelo2 %>% fit(price ~ poly(x, 8), data = diamondsinho) + + +# predicoes --------------------------------------------------------------- +diamondsinho_com_previsao <- diamondsinho %>% + mutate( + price_pred1 = predict(ajuste_modelo1, new_data = diamondsinho)$.pred, + price_pred2 = predict(ajuste_modelo2, new_data = diamondsinho)$.pred + ) + +# qualidade dos ajustes e graficos ---------------------------------------- +# Métricas de erro +diamondsinho_com_previsao_longo <- diamondsinho_com_previsao %>% + tidyr::pivot_longer( + cols = starts_with("price_pred"), + names_to = "modelo", + values_to = "price_pred" + ) + +set.seed(3) +# "dados novos chegaram..." +diamondsinho_novos <- diamonds %>% + filter(x > 0, x < 8) %>% + sample_n(20) + +# predicoes --------------------------------------------------------------- +diamondsinho_novos_com_previsao <- diamondsinho_novos %>% + mutate( + price_pred1 = predict(ajuste_modelo1, new_data = diamondsinho_novos)$.pred, + price_pred2 = predict(ajuste_modelo2, new_data = diamondsinho_novos)$.pred + ) +``` + + +# Overfitting (sobreajuste) + +- Acontece quando um modelo funciona muito pior quando usado com dados novos quando + comparado com a performance nos dados em que foi treinado. +- Uma das principais preocupações quando ajustamos modelos em ML. +- **Solução**: Sempre testar o modelo com dados 'novos'. + +--- + +# Overfitting (sobreajuste) + +```{r, eval=TRUE, echo=FALSE, fig.retina=4, fig.width=10} +# Pontos observados + curva da f +set.seed(3) +dfzim <- diamondsinho_com_previsao +dfzim_maior <- data.frame(x = seq(from = 4.5, to = 7.5, length.out =100))%>% + mutate( + price_pred1 = predict(ajuste_modelo1, new_data = .)$.pred, + price_pred2 = predict(ajuste_modelo2, new_data = .)$.pred + ) + +setinha <- annotate( + geom = "curve", + arrow = arrow(type = "closed", angle = 10, length = unit(0.3, "inches"), ends = "first"), + colour = "grey", + x = dfzim$x[5], + y = dfzim$price[5] + 650, + xend = 5.3, + yend = 13000 + ) +rotulozinho <- annotate( + "text", + size = 6, + x = 5.3, + y = 13000, + hjust = 1.01, + label = "base de treino", + colour = "grey" + ) +pt1 <- dfzim %>% + ggplot() + + geom_point(aes(x, price), size = 4, alpha = 0.2) + + ylim(c(-10, 15000)) + + xlim(c(4.5,8)) + + setinha + + rotulozinho +pt1 +``` + +--- + +# Overfitting (sobreajuste) + +```{r, eval=TRUE, echo=FALSE, fig.retina=4, fig.width=10} +# Pontos observados + curva da f + +pt2 <- pt1 + + geom_line(aes(x, price_pred2, color = 'modelo2'),data = dfzim_maior, size = 1, show.legend = FALSE) +pt2 +``` + +--- + +# Overfitting (sobreajuste) + +```{r, eval=TRUE, echo=FALSE, fig.retina=4, fig.width=10} +# Pontos observados + curva da f +pt3 <- pt1 + + geom_line(aes(x, price_pred1, color = 'modelo1'), data = dfzim_maior, size = 1, show.legend = FALSE) +pt3 +``` + +--- + +# Overfitting (sobreajuste) + +```{r, eval=TRUE, echo=FALSE, fig.retina=4, fig.width=10} +# Pontos observados + curva da f +set.seed(4) +dt <- diamondsinho_novos_com_previsao %>% filter(x < 8) %>% ungroup() %>% sample_n(20) +setinha_vermelha <- annotate( + geom = "curve", + arrow = arrow(type = "closed", angle = 10, length = unit(0.3, "inches"), ends = "first"), + colour = "red", alpha = 0.5, + x = dt$x[18], + y = dt$price[18] + 650, + xend = 5.0, + yend = 9000 + ) +rotulozinho_vermelho <- annotate( + "text", + size = 6, + x = 5.0, + y = 9000, + hjust = 1.01, + label = "base de teste\n(dados novos)", colour = "red", alpha = 0.5 + ) +pt4 <- pt3 + + geom_line(aes(x, price_pred2, color = 'modelo2'), data = dfzim_maior, size = 1, show.legend = FALSE) + + geom_point(aes(x, price), size = 4, data = dt, colour = "red", alpha = 0.5)+ + geom_point(aes(x, price), size = 1, data = dt, colour = "red", alpha = 1) + + setinha_vermelha+ + rotulozinho_vermelho +pt4 +``` + + + +--- + +# Overfitting (sobreajuste) + +Intuição + +![scatter_eqm](static/img/overfiting_scatter_eqm.gif) + + +--- + +# Overfitting (sobreajuste) + +Intuição + +![scatter_eqm](static/img/overfiting_scatter_eqm_logistic.gif) + + +--- + +# Dados novos vs antigos + +- **Base de Treino** (dados antigos): a base de histórico que usamos para ajustar o modelo. + +- **Base de Teste** (dados novos): a base que irá simular a chegada de dados novos, "em produção". + +.pull-left[ + +```{r, eval = FALSE, echo=TRUE} +initial_split(dados, prop=3/4) +``` + + +> "Quanto mais complexo for o modelo, menor será o **erro de treino.**" + +> "Porém, o que importa é o **erro de teste**." + +] + +.pull-right[ + + +] + +--- +class: middle, center + +## Exemplo 02 + +--- + +# Dados novos vs antigos + +## Estratégia + + +#### 1) Separar inicialmente a base de dados em duas: **treino** e **teste**. + +```{r, eval = FALSE, echo=TRUE} +initial_split(dados, prop=3/4) # 3/4 de treino aleatoriamente +initial_time_split(dados, prop=3/4) # 3/4 de treino respeitando a ordem +``` + +A base de teste só será tocada quando a modelagem terminar. Ela nunca deverá influenciar nas decisões que tomamos durante o período da modelagem. + +palavra-chave: **data leakage** ou **vazamento de informação** + + +--- + +## Regularização + +**Objetivo da Regularização:** Oferecer um parâmetro (um valor que podemos mudar) para termos controle sobre a **complexidade** da $f(x)$ e assim evitar o *sobreajuste*. + +No exemplo da regressão linear, haverá um valor $\lambda$ que chamaremos de "hiperparâmetro" da regressão. Iremos chutar diferentes valores de $\lambda$ até encontrar a melhor $f(x)$. + +--- + +## Regularização - LASSO + +Relembrando o nossa **função de custo** RMSE. + +$$RMSE = \sqrt{\frac{1}{N}\sum(y_i - \hat{y_i})^2} = \sqrt{\frac{1}{N}\sum(y_i - \color{red}{(\hat{\beta}_0 + \hat{\beta}_1x_{1i} + \dots + \hat{\beta}_px_{pi})})^2}$$ + +Regularizar é "não deixar os $\beta's$ soltos demais". + +$$RMSE_{regularizado} = RMSE + \color{red}{\lambda}\sum_{j = 1}^{p}|\beta_j|$$ + +Ou seja, **penalizamos** a função de custo se os $\beta's$ forem muito grandes. + +**PS1:** O $\color{red}{\lambda}$ é um **hiperparâmetro** da Regressão Linear. + +**PS2:** Quanto maior o $\color{red}{\lambda}$, mais penalizamos os $\beta's$ por serem grandes. + +--- + +## Regularização - LASSO + +Vamos testar diversos valores para $\color{red}{\lambda}$ até encontrar o que dá o menor erro de teste. + + + + +--- + +## Regularização - LASSO + +Conforme aumentamos o $\color{red}{\lambda}$, forçamos os $\beta's$ a serem cada vez menores. + + +![scatter_eqm](static/img/betas.png) + + +.footnote[ +Ver [ISL](https://www.ime.unicamp.br/~dias/Intoduction%20to%20Statistical%20Learning.pdf) página 219 (The LASSO). +] + +--- + +# Hiperparâmetros + +São parâmetros que têm que ser definidos antes de ajustar o modelo. Não há como achar o valor ótimo diretamente nas funções de custo. Precisam ser achados **na força bruta**. + +Exemplo: `lambda` da penalização do LASSO (`penalty`) + + +.pull-left[ + +``` +linear_reg(penalty = 0.0) +linear_reg(penalty = 0.1) +linear_reg(penalty = 1.0) +linear_reg(penalty = tune()) +``` + +] + + +--- + + +## Problema! + +Teremos que testar muitos 'lambdas'. Podemos desgastar a base de teste (erro de teste vai ter alta variabilidade). Para isso, inventaram a estratégia de reamostragem que oferece uma estimativa do erro de predição (erro de teste) de forma mais confiável. + + +--- + +# Cross-validation (validação cruzada) + +**O que Validação cruzada faz:** estima (muito bem) o erro de predição. + +**Objetivo da Validação cruzada:** encontrar o melhor conjunto de hiperparâmetros. + +### Estratégia + +.pull-left[ + +1) Dividir o banco de dados em K partes. (Por ex, K = 5 como na figura) + +2) Ajustar o mesmo modelo K vezes, deixar sempre um pedaço de fora para servir de base de teste. + +3) Teremos K valores de erros de teste. Tira-se a média dos erros. + +] + +.pull-right[ + + +] + +--- + +# Cross-validation (validação cruzada) + + +```{r, echo = TRUE, eval=FALSE} +vfold_cv(cars, v = 5) +``` + +```{r, echo = FALSE} +library(rsample) +set.seed(1) +cars_cv <- rsample::vfold_cv(cars, v = 5) %>% + mutate( + n_treino = map_dbl(splits, ~nrow(as.data.frame(.x))), + n_teste = map_dbl(splits, ~nrow(assessment(.x))), + regressao = map(splits, ~lm(dist ~ speed, data = .x)), + rmse_teste = map2_dbl(regressao, splits, ~ { + df <- rsample::assessment(.y) %>% + mutate(pred = predict(.x, newdata = rsample::assessment(.y))) + + round(sqrt(mean((df$dist - df$pred)^2)), 2) + }) + ) +cars_cv +``` + +ERRO DE VALIDAÇÃO CRUZADA: $$RMSE_{cv} = \frac{1}{5}\sum_{i=1}^{5}RMSE_{Fold_i} = 15,1$$ + +--- + +# Cross-validation (validação cruzada) + +### Esquema das divisões de bases: + + + +.footnote[ +Fonte: [bookdown.org/max/FES/resampling.html](https://bookdown.org/max/FES/resampling.html) +] + +--- + +# Cross-validation (validação cruzada) + +Em pseudo-código: + +``` +K <- 5 + +fold <- sample.int(K, nrow(mtcars), replace = TRUE) +for (k in 1:K) { + train <- mtcars[fold != k,] + valid <- mtcars[fold == k,] + + # ajusta_modelo(train) + # metrics(valid) +} +``` + +--- +class: middle, center + +## Exemplo 03 + +--- + +## Regularização - Ridge + +No LASSO, usamos o módulo dos betas para fazer a regularização. +É possível fazer também usando o quadrado dos coeficientes: + +$$RMSE_{Ridge} = RMSE + \color{red}{\lambda}\sum_{j = 1}^{p}\beta_j^2$$ + +Também é possível misturar os dois + +$$RMSE_{regularizado} = RMSE + (\alpha) \times \color{red}{\lambda}\sum_{j = 1}^{p}|\beta_j| + (1 - \alpha) \times \color{red}{\lambda}\sum_{j = 1}^{p}\beta_j^2$$ + +Nessa definição $\alpha$ é chamado de 'mixture' (mistura). Quando $\alpha=1$ temos o LASSO e quando $\alpha=0$ temos Ridge. O $\alpha$ também pode ser tunado. + +--- + +## Ridge vs LASSO + +O LASSO tem uma propriedade muito interessante quando +comparada ao Ridge. Por razões matemáticas, ele consegue produzir estamativas esparsas, isto é, alguns coeficientes podem ser exatamente 0. + + + +.footnote[ + Fonte: [ISLR pag. 224](https://web.stanford.edu/~hastie/ISLRv2_website.pdf) +] + +--- +class: middle, center + +## Exercício 01 + +--- + +## Resumo dos conceitos + + + diff --git a/slides/01-intro-ml.html b/slides/01-intro-ml.html new file mode 100644 index 0000000..5217092 --- /dev/null +++ b/slides/01-intro-ml.html @@ -0,0 +1,1590 @@ + + + + Introdução ao Machine Learning + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/slides/01-intro-ml.pdf b/slides/01-intro-ml.pdf new file mode 100644 index 0000000000000000000000000000000000000000..45de777997fc2b0a87f9e39f1d450ba5db873a0a GIT binary patch literal 5328715 zcmeFZ2|U&5`#*drGe$F6lJ=4|R3sx2St3%DeLI*);)KFUWN8{@ixg5sB4kgJCCiMW zQjz3n!$`6mr7RV~b6xl6XqlPs_xt<(UcdkIyk5`qe9Ae;=W{RDeqZ-}y^m!(G&Zl6 zk@}f$Sp&PfjZa2&ji{@w6Q7cj^d>j^ogS`kqT-wOxVbtzGMy#(q<6Tv?qb^6!%ahm 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