Business Data Science: Combining Machine Learning and Economics to Optimize, Automate, and Accelerate Business by Matt Taddy

(New York: McGraw Hill, 2019), 331


Contents


Resources

If Latex does not render, you can download a PDF of these notes here.
  • The author's data and R scripts for the book is on GitHub (see also code for MBA course).
  • My code to accompany these notes is on GitHub.
  • Amazon author interview discussing concepts from the book.

Introduction

Summary: Our goal is to produce interpretable models that translate data into insights for decision-making. The modern methods of business data science are characterized by the addition of big data and machine learning to classical statistical and economic methods.

Code for this section is here.

  • The Goal: produce an interpretable model that translates raw data into information relevant to decision-making; project information into a low-dimensional space that contains key insights for decision making (3-4)

    • Motivating example: visualized CAPM outputs give a richer view for decisions making than just a messy plot of returns (Figure I.3, reproduced here)

  • "Modern methods" are distinguished by big data and machine learning

    • Data Science ≈ statistics + BD + ML

    • Business Data Science ≈ statistics + BD + ML + economics + econometrics + business context

  • Big Data: data can be "big" in terms of both volume and complexity

    • Big (volume) Data is where the scale swamps RAM and requires piping by data engineers

    • Big (complexity) Data is big dimension data where the assumptions of classical statistics break down ("big p" problems)

  • Machine Learning: automatically build predictions from complex data

    • Key techniques include lasso regularized regression, random forests, neural networks (295)

    • Focus is to maximize predictive performance on out-of-sample data

    • Limited structural interpretability: black box for making predictions when the future follows the same patterns as the past (with the implicit warning about the danger of changing patterns)

    • Structural analysis refers to building analytically from theory, as compared with the pragmatic, black-box prediction of machine learning

    • Good data science then is having an overall understanding of the domain to know the appropriate prediction tasks to throw at ML, and the structural problems to address with classical economics and statistics

    • "A policy-maker who can deploy ML to solve the many prediction tasks that they face will be able to automate and accelerate their decision process." (7)

    • ML prediction tools should be part of a larger system with goals beyond pure prediction

  • Computation

    • This book uses R, but the key point is that "anyone working with data will need to continue learning and updating their computational (and methodological) skills"; best way to learn is by doing (11)

Chapter 1: Uncertainty

Summary: This chapter introduces nonparametric ("data driven", frequentist) and parametric ("theoretical", Bayesian) approaches to quantifying uncertainty. The Bootstrap is a flexible nonparametric method that works by resampling with replacement. The Benjamini-Hochberg algorithm provides a method of selecting variables by ranked p-value based on the desired false discovery rate. Finally, we learn about the Bayesian framework for combining assumptions with evidence.

  • Parametric vs Nonparametric

    • Parametric: "theoretical"

    • conditional on assumed true model

    • Nonparametric: "data driven"

    • allows for model misspecification

Parametric Nonparametric
Quantifies uncertainty Quantifies uncertainty
"Theoretical" "Data-driven"
Bayesian Frequentist
Assume CLT/Gaussian Use the Bootstrap
Specify distribution More flexible
"Ideal" for theory "Ideal" for decision-making
High-dimensional data ok Requires low-dimensional data $n >> p$
  • Frequentist vs Bayesian

    • Frequentist: classical uncertainty

    • "If I were able to see a new sample of data generated by the same processes and scenarios as my current data, how would my estimates change?"

    • Bayesian: mathematical framework of beliefs (more below)

    • "If you believe A and then you observe B, you should update your beliefs to C."

  • Central Limit Theorem (CLT): the average of independent random variables becomes normally distributed if your sample size is large enough
  • The Bootstrap: uses resampling (with replacement) from your current sample to mimic the sampling distribution and introduce variability

    • use the Bootstrap because theoretical Gaussian distributions derived from the CLT are not valid for many complex settings (i.e. number of model parameters large relative to number of observations)

    • the Bootstrap will work in many settings where theory is either unavailable or incorrect (if the Bootstrap fails, there probably isn't a good theoretical replacement)

    • an alternative is the Parametric Bootstrap: generate new data by drawing from a fitted model (the results are sensitive to how well the model represents reality, but this is a practical option when more robust procedures are impossible)

  • p-values: represents how rare or strange your sample would be if the null hypothesis is true

    • the proportion of times that you would wrongly reject your safe null if the test statistic you've observed is enough to lead you to adopt the alternative

    • measures the probability mass in the tails past your observed test statistic

  • Benjamini-Hochberg (BH) FDR Control: controls your false discovery rate (FDR) by defining a cutoff on the ranked list of p-values from your model

    • $FDR=\mathop{\mathbb{E}} \left[ \frac{FalsePositives}{TestsCalledSignificant} \right]$

    • Select your target $FDR$ of $q$, and keep all p-values such that $p \leq q\frac{k}{N}$

    • Gives a decent (often conservative) guess at FDR

  • Bayesian Inference: the mathematical framework of beliefs

    • characterizes probabilities over models and parameters by appealing to the idea of subjective beliefs rather than repeated trials

    • quantification of risks and expected rewards is inherently Bayesian

    • "If you believe A and then you observe B, you should update your beliefs to C."

    • provides a framework for combining assumptions with evidence

    • mechanically works with combination of prior distributions and likelihood (the probability of the data you have observed given a fixed set of mode parameters)

    • inherently parametric since you specify a model and then update view of uncertainty based on new data

Chapter 2: Regression

Summary: The basic linear regression model (and its logistic counterpart for binary response) are key data science tools. This chapter provides details and examples of their use, along with uncertainty estimation using nonparametric methods such as the bootstrap.

Code for this chapter is here.

  • Linear models work with averages and lines: consider simple linear regression of the form $y = \alpha + x\beta$, or logarithmic: $\log(y) = \alpha + \beta \log(x) + \epsilon$

    • The log-log model is intuitive: $y$ increases by $\beta$% for every 1% increase in $x$, where $\beta$ is the elasticity

  • This is how to understand the coefficients of the glm object:

    • reg = glm(log(sales) ~ log(price) + brand, data=data)

    • beta <- coef(reg)

    • beta[1] = $\alpha$ (intercept for base: brand=dominicks)

    • beta[2] = $\beta$ (slope)

    • beta[3] = $\alpha{mm}$ (incremental intercept for brand=minute.maid)

    • beta[4] = $\alpha{t}$ (incremental intercept for brand=tropicana)

  • This is how to understand the coefficients of the glm object with interactions:

    • reg_interact = glm(log(sales) ~ log(price)*brand, data=data)

    • beta <- coef(reg_interact)

    • beta[1] = $\alpha$ (intercept for base: brand=dominicks)

    • beta[2] = $\beta$ (slope for base: brand=dominicks)

    • beta[3] = $\alpha{mm}$ (incremental intercept for brand=minute.maid)

    • beta[4] = $\alpha{t}$ (incremental intercept for brand=tropicana)

    • beta[5] = $\beta{mm}$ (incremental slope for brand=tropicana)

    • beta[6] = $\beta{t}$ (incremental slopee for brand=tropicana)

  • Logistic Regression (page 50-53) uses the logit link function to scale probabilities between 0 and 1:

    • $p(y=1|x) = \frac{e^{x' \hat{\beta}}}{1 + e^{x' \hat{\beta}}}$

    • Logistic regression is a linear model for log odds (where odds = probability it happens over probability it doesn't):

    • $\log \left[ \frac{p}{1-p} \right] = \beta{0} + \beta{1}x{1}... + \beta{p}x{p}$



      • Use family='binomial' for logistic regression


      • "y ~ ." to regress y on to all variables in the data



    • Interpreting coefficients: $e^{\beta k}$ is the multiplicative effect for a unit increase in $x{k}$ on the odds for the event $y=1$.

    • When predicting, call type='response' to run predictions through the logit link as $e^{x' \hat{\beta}} / (1 + e^{x' \hat{\beta}})$.

  • Deviance and Likelihood (page 53-57)

    • Likelihood is the probability of your data given parameters (want as big as possible).

    • Deviance measures the distance between data and fit (want as small as possible: the cost to be minimized).



      • $Deviance = -2\log{Likelihood} + C$


      • $C$ represents the fully saturated model where you have as many parameters as observations.



    • Maximum likelihood estimation (MLE): to minimize deviance in the equation below we need to minimize the sum of squared errors, so MLE = OLS (ordinary least squares):



      • $dev(\beta) \propto \sum{i=1}^{n}(y{i}-x^{'}_{i}\beta)^{2}$



    • Residual deviance: $D=dev(\hat{\beta})$ is deviance to fitted model.

    • Null deviance: $D{0}=dev(\beta=0)$ is deviance for null (basic) model where all $\hat{y}{i}=\bar{y}$

    • The difference between $D$ and $D{0}$ is due to information contained in the covariates. $R^{2}$ is the proportion of deviance explained by $x$:



      • $R^{2} = \frac{D{0}-D}{D{0}} = 1 - \frac{D}{D{0}}$


      • This general form allows you to compute $R^{2}$ for almost any machine learning model (rather than the form specific to the linear regression: $R^{2} = \frac{SSE}{SST}$).



  • Other R summary output parameters:

    • Dispersion parameter: measure of variability around the fitted conditional means, estimate for error variance $\sigma^{2}$.

    • Degrees of freedom: actually residual degrees of freedom, or number of observations less number of parameters

    • Degrees of freedom for the rest of the book refers to model degrees of freedom, or number of parameters in the model

  • Regression Uncertainty (page 58-61)

    • Since "standard" standard errors are sensitive to misspecification, we can use nonparametric methods to better estimate uncertainty

    • The Bootstrap: resample with replacement and use the uncertainty across samples as an estimate of actual sampling variance

    • Sandwich variance estimator to get HC standard errors (heteroskedastic consistent rather than assuming homoskedastic), use the R AER package

    • For OLS, HC standard errors approximate and are a fast alternative to bootstrapping

  • Space and Time (page 61-67)

    • Previous discussion assumes independence between observations.

    • Since that's not the case, we can include variables behind dependence in the same GLM framework.

    • Rather than building by hand, include many variables and use later Regularization and Model Selection chapters to select the appropriate ones to use.

    • When adding variables, proceed hierarchically: include larger (year, state) variables for any smaller ones (month, city)

    • Autocorrelation occurs frequently with time series data that has local dependence. The autocorrelation function (ACF) tracks lag correlations.



      • Model this type of data with a Random Walk (a form of autoregressive (AR) model), first order form of $AR(1)$:


      • $AR(1): y{t} = \beta{0}+\beta{1}y{t-1}+\epsilon{t}$


      • if $|\beta{1}| = 1$, random walk (model with returns rather than values like the stock market)


      • if $|\beta{1}| > 1$, series explodes (you might be missing a trend variable, otherwise challenging)


      • if $|\beta_{1}| < 1$, series reverts to mean (common and useful)


      • You can use $AR(p)$ for higher lags and model selection methods to choose the appropriate lag.


      • Spatial autoregressive (SAR) models to include spatial neighbors (similar to temporal neighbors)



Chapter 3: Regularization

Summary: Regularization allows us to develop candidate models and select the best model for OOS performance. We add a penalty term and then minimize the penalized deviance; a common penalty construction is the Lasso. Then we can select the optimal penalty weight—$\lambda$—using cross validation or information criteria as our model selection process. Finally, we can approximate the uncertainty of such a model using a parametric bootstrap or subsampling.

  • Regularization context: provides a framework when working with high-dimensional data to develop candidate models and then select the best model to minimize error on out-of-sample data (needed to avoid overfit)

    • Regularization penalizes model complexity to stabilize the system, minimizes penalized deviance

    • "Regularization is the key to modern statistics" (77)

    • "Regularization is trading variance (noise) for bias" (91)

  • The only $R^{2}$ we care about is out-of-sample $R^{2}$

    • In-sample $R^{2}$ is always increased with more variables, making it look artificially good (it can even produce a negative out-of-sample $R^{2}$, or model that performs worse than no model at all)

  • Cross validation: use out-of-sample experiments to choose the best model

    • Use data to select the best model

    • K-fold out-of-sample cross-validation: split data into K folds, fit coefficients on everything except kth fold, then record $R^{2}$ for the left-out kth fold

  • Backward stepwise regression: start with full model and cut it back to size

    • Start with full model, cut back variables below $\alpha$ using BH FDR control

    • This is generally not ideal because it does not handle multicollinearity (correlation between inputs) well

  • Forward stepwise regression: build from simplicity to complexity, greedy search strategy, fast and stable, stable
  • Regularization minimizes penalized deviance:

    • $\hat{\beta} = \mbox{argmin} \left{-\frac{2}{n} \log \mbox{lhd} (\beta) + \lambda \sum{k}{c(\beta{k})} \right}$ where $\lambda \sum{k}{c(\beta{k})}$ is the penalty term and $c(\beta_{k})$ is the cost on the size of the coefficient

    • This accounts for both the estimation cost (deviance, distance between data and model) and the testing cost (cost of $\beta \neq 0$)

  • The lasso has $c(\beta{k})=|\beta|$

    • Default because least bias on large signals while retaining the stability of a convex penalty, also automatic variable screening since some $\beta$ will be exactly zero

    • Provides an enumeration of candidate models (different values of $\lambda$), then use model selection to choose the best $\lambda$

    • Lasso regularization path: start with $\lambda$ such that $\hat\beta{1}=0$, then shrink $\lambda$ to reduce the penalty on $\beta$ and iteratively add complexity to the model

    • $\lambda$ operates on all $\beta$, so typically scale by $\mbox{sd}(x)$ so that the penalty on $\beta$ is measured on the scale of 1 standard deviation change in $x$

Model Selection: use cross validation (CV) or information criteria (IC) to select the best $\lambda$

  • Recall: $\lambda$ is the penalty weight (signal-to-noise filter like a radio squelch)
  • K-Fold CV Lasso: obtain candidate models from lasso, fit lasso path on data except kth fold and calculate deviance on kth fold, and choose $\lambda$ by either CV-min (recommended) or CV-1se (more conservative)

    • Cross validation answers: "Which model does best in predicting unseen data?"

    • CV is a computational experiment to approximate OOS errors

  • Information Criteria (IC): analytic approximation of OOS errors, many flavors (AICc, AIC, BIC, etc.)

    • Akaike's criterion: $\mbox{AIC} = \mbox{deviance} + 2df$ where deviance is calculated in-sample and $df$ are your model degrees of freedom; true for low-dimensional models

    • Corrected AIC: $\mbox{AICc} = \mbox{deviance} + 2df \frac{n}{n-df-1}$, should always be used over AIC: works where AIC doesn't and provides the same answer where it does

    • Bayes criterion: $\mbox{BIC} = \mbox{deviance} + \log(n) \times df$, attempts to get at the "true" model and is more conservative

  • If you have time and answer is important, do CV. AICc is fast and stable. Typically use a combination of the two.

Lasso Uncertainty

  • Uncertainty quantification not easy because of penalty term and high-dimensional objects, but can use parametric bootstrap, subsampling, or sample splitting (ch 6)
  • Parametric Bootstrap: rather than resampling with replacement (as in nonparametric bootstrap, which will overfit), generate new data from a model with less bias, say $\bar\lambda \approx \lambda/4$

    • Drawback: relies upon the correctness of your data generating process

  • Subsampling: re-estimate your target using without-replacement subsamples

    • Estimates are based on smaller sample than you actually have, so must assume a learning rate to adjust a size-m uncertainty for size-n sample estimate (typically $\sqrt{n}$)

  • Both are approximation tools that should be treated with skepticism

Chapter 4: Classification

Summary: K-Nearest Neighbors is a common classification algorithm but not suitable for large datasets. For practical applications we focus on predicting *probabilities using either Multinomial Logistic Regression, or Distributed Multinomial Regression which uses a Poisson distribution to enable distributed computation.*

  • K-Nearest Neighbors: what is the most common class for observations around x?

    • Drawbacks: units matter (can scale), results unstable as a function of K, cross validation doesn't work well, computationally expensive

    • Therefore, we will focus on methods and models for probability

  • Decisions have costs: probabilities allow us to compute expected loss

    • $FPR = \text{False Positive Rate} = \frac{\text{expected # false positives}}{\text{# classified positive}}$

    • $FNR = \text{False Negative Rate} = \frac{\text{expected # false negatives}}{\text{# classified negative}}$

    • Sensitivity: proportion of true $y=1$ classified as such

    • Specificity: proportion of true $y=0$ classified as such

    • ROC Curve plots $sensitivity$ vs $1-specificity$

  • Great quote (114):

    • >It is dangerous to make changes to future behavior based on a naive analysis of past data.

  • Multinomial Logistic Regression uses the multinomial logit or softmax function: $e^{z{j}} / \sum{k} e^{z{k}}$ --> can predict with this using cv.glmnet(...family="multinomial")

    • $e^{x'\beta{k}}$ acts as an intensity for each class

  • Distributed Multinomial Regression uses a Poisson distribution (count data) to improve the performance of MLR

    • Using Poisson distribution allows you to improve prediction performance by setting a different $\lambda{k}$ for each class, and compute each $\hat{\beta{k}}$ in parallel (R's parallel library)

  • Distribution & Big Data

    • parallel if algorithm can do many computations at once

    • distributed when each computation can work with a subset of data

    • MapReduce (MR) can be applied to DMR

Chapter 5: Experiments

Summary: Experiments allow us to predict a different future from the past after we take action to change it. Randomized Controlled Trials—or AB Testing—are the gold standard, but we can also approximate causal impact using Difference-in-difference for adjacent markets as an example, Regression discontinuity when treatment occurs at a threshold, or Instrumental Variables to understand causal inference from upstream randomness.

  • Experiments allow us to predict a future that is different from the past (because you take actions to make it different, i.e. counterfactuals).
  • Randomized Controlled Trials—or AB Testing—are the gold standard for estimating counterfactuals

    • AA tests are good practice to ensure no issues with randomization (you expect results to be the same)

    • AB tests are completely random so it is easy to estimate the Average Treatment Effect (ATE) on the response, given as the mean difference in response: $ATE = \mathbb{E}[y|d=1] - \mathbb{E}[y|d=0] = \bar{y{1}} - \bar{y{0}}$

    • You can reweight your sample if certain sample segments are underrepresented relative to the population

    • Common issues with randomized trials include: imperfect randomization and dependence between units/observations

  • Difference-in-difference and Regression discontinuity allow you to recover causal treatments in situations where you can't perform a randomized trial
  • Difference-in-difference (diff-in-diff) applies when you can isolate pretreatment differences, as in different markets. This is only as reliable as the two group are comparable.
  • Regression discontinuity applies where treatment is determined by an arbitrary threshold and we can observe observations on either side of the threshold (i.e. grate thresholds, income thresholds, etc.)

    • Make a continuity assumption and extrapolate on either side of the threshold

    • Fit regression models on either side of the threshold and observe the difference in their predictions at the threshold to show impact of the treatment

    • Instrumental Variables are upstream sources of randomness that can mimic the effect of an experiment to demonstrate causality



      • endogeneity: when the policy (treatment) and error are correlated, the "omitted variable bias" requiring the use of instrumental variables


      • example: relationship between airline prices and demand, both of which are high during the holidays



```mermaid
graph LR

id1(z=IV)
id2(x=observed covariate)
id3(p=policy/treatment)
id4(y=response)
id5(e=unobserved error)

id1 --> id3
id2 --> id3
id5 --> id3
id5 --> id4
id3 --> id4
id2 --> id4
```

  • Use two-stage least squares (2SLS) to recover causal effects from IV variation: $\mathbb{E}[y|z]=\gamma\mathbb{E}[p|z]$

    • First fit OLS for p on x and z

    • Next fit OLS for response onto the predicted policy and the covariates to estimate $\mathbb{E}[y|\hat{p}{i},x{i}]=\alpha{y}+\hat{p}{i}\gamma + x'{i}\beta{y}$ where $\gamma$ is the causal effect of p on y

    • in R, use ivreg function in AER package, with | to separate first and second stage inputs

Chapter 6: Controls

Summary: When we can't run experiments, we can still get at causality through observational studies. If we include all variables that impact the treatment, we can interpret classical models causally (Linear Treatment Effects). We can also use Synthetic Controls to asses the impact of a treatment when other regions were not treated.

  • When we can't run experiments, we can use on observational studies which depends upon the assumption of conditional ignorability (CI): that you have controlled for all variables that influence both the treatment and response
  • Linear Treatment Effects (LTE) model: if x contains all variables that influence d and y, then $\gamma$ can be interpreted causally

    • $y = d\gamma + x'\beta + \varepsilon$, $\varepsilon|d, x = 0$

    • $d = x'\tau + v$, $v|x=0$

  • Adapt lasso and CV for causal inference under CI for high-dimension problems: LTE Lasso Regression or Propensity Models for binary treatments
  • Use Sample Splitting (or Orthogonal Machine Learning) for inference and uncertainty quantification: split sample into two pieces, model selection on one and standard inference on the second
  • Heterogeneous Treatment Effects (HTE) deals with the problem of treatment being different for different subjects

    • price elasticity is a common use case of this type model (see beer sales example)

  • Synthetic Controls allow us to estimate the impact of a treatment by comparing one region to other regions that did did not have the treatment

    • You need to assume independence between regions and stationary structural relationships, and this can be used in conjunction with observed controls

    • You can predict each of the unchanged regions (placebos) as a means of approximating the error

  • Some strategies to deal with missing data include:

    • create new category for missing values (categorical variables)

    • impute missing values with the mean or with zero (numeric variables)

Chapter 7: Factorization

Summary: Data Science is effectively *dimension reduction, and factorization is one tool for breaking the expectation for each x into the sum of a small number of factors. Principal Component Analysis is a primary tool for factorization which projects the data onto orthogonal dimensions with decreasing variance.*

  • Clustering (including K-Means) collects observations into groups

    • K-means can generate different answers each time you run it (there can be multiple local minimums), so treat it more as an exploratory tool

  • Principal Component Analysis (PCA) identifies the dimensions with the highest variance

    • Think about PCA as:



      • repeatedly fitting a regression onto the best possible factors to explain the current residuals


      • rotating the axes of the data for the projections with the highest variance



    • You can summarize most of the variation with the first K components

    • Use prcomp(x, scale=TRUE) to compute PCA in R

    • PCA can provide (approximate) interpretable results

  • Principal Component (Lasso) Regression (PCR)

    • Instead of regressing y onto x, regress y onto v from the PCA

    • This is beneficial because PCA reduces dimension, PCs are independent (removes multicollinearity), and you can use the results of unsupervised PCA on a large bank of unlabeled data on a smaller supervised regression

    • Use Lasso regression and then you can regress y onto both x and v

  • Sometimes v is not relevant to both x and y, so make this true using Partial Least Squares (PLS):

    • This is a special case of Marginal Regression (MR), a strategy for supervised learning in ultra-high ($p\gg n$) dimensions: regress y on to each dimension of x independently and use the resulting coefficients to map from x to v

    • PLS repeats MR for multiple iterations ("boosted marginal regression")

    • Boosting: repeatedly apply residuals from the previous fit of a simple algorithm

    • PLS often offers greater interpretability than Lasso

Chapter 8: Text as Data

Summary: Once raw text is tokenized it can be treated with many of the data science methods we have learned. Textual analysis is often messy or subjective, so it is wise to use it as a supplement to a larger system.

  • Tokenization translates raw text into counts of words/phrases that can then be used by data science
  • Use Stemming to remove word endings and keep only the root of the word
  • Text Regression uses this data as an input for lasso or other regression techniques
  • Topic Models are multinomial factor models that often lead to more interpretable factorization
  • Multinomial Inverse Regression (MNIR) complements text regression and topic modeling and is useful for sorting through a large number of related influences on text and categorizing according to these factors
  • Collaborative Filtering (the Netflix problem) seeks to make recommendations, often accomplished with Market Basket Analysis which computes the lift from a predecessor
  • Word Embedding imposes spatial structure on words allowing you to get at relationships of meaning and context when making predictions

Chapter 9: Nonparametrics

Summary: Nonparametric methods don't assume any relationships like parametric (linear) methods but given enough data can learn these relationships. Decisions trees and the averaging these into Random Forests are the most common and flexible methods and produce excellent results out of the box.

  • Nonparametric algorithms make fewer assumptions about the relationship between x and y, and in fact learn the true relationship with enough data (assuming independence between observations). Requires low dimensional data: $p\ll n$
  • Decision Trees use a hierarchical series of ordered steps (decision nodes) to map inputs to outcomes
    ```mermaid
    graph LR

id1(Wake Up)
id2(>70% Rain)
id3(<70% Rain)
id4(Umbrella)
id5(>30% Rain)
id6(Cloudy)
id7(Umbrella)
id8(Sunny)
id9(No Umbrella)
id10(<30% Rain)
id11(No Umbrella)

id1 --> id2
id1 --> id3
id2 --> id4
id3 --> id5
id5 --> id6
id6 --> id7
id5 --> id8
id8 --> id9
id3 --> id10
id10 --> id11
```

  • Classification and Regression Tree (CART) is a method of fitting trees to minimize a loss function (rather than based on $x'\beta$ like linear models, predicted $\hat{y}$ is defined via thresholds on splitting the dimensions of $x$)

    • Split recursively until you reach a node of a specified minimum size

  • Random Forests perform bagging (bootstrap aggregating) to effectively average a large number of trees: "nothing performs better out of the box on big data prediction problems"

    • Forest predictions are the average of individual tree predictions

    • Uncertainty bounds (defined as the min/max of individual trees) are adaptive based on how far apart individual trees are in different regions

    • You lose the interpretability of single trees, but can get some intuition around variable importance calculated as the increase in error that occurs when a variable is not used to define tree splits

    • Random forests can be computed efficiently using Empirical Bayesian Forests which keep the same trunk (first several splits) for all trees and only allow variation lower down

  • "More data always wins...For prediction tasks, never reduce the amount of data you can work with to fit some fancy but computationally costly model—you're better off with a simple but flexible model fit to as much data as you can get your hands on." (279)
  • Causal Trees are a tree-based model that is well-suited for modeling heterogeneous treatment effects in each child node
  • Gradient Boosted Machines iteratively estimate a sequence of shallow trees each trained to predict the residuals of the previous tree (requires CV to decide when to stop boosting)
  • Gaussian Processes smooth predictions across observations according to distances between the inputs

Chapter 10: Artificial Intelligence

Summary: Artificial Intelligence can replace people for certain tasks. This is achieved by decomposing complex tasks into sub-problems that can be solved with general-purpose machine learning tools, especially deep neural nets.

  • Let Artificial Intelligence be systems that ingest human-level knowledge to automate and accelerate tasks previously performed only by humans

    • Seeks to solve complex problems by using domain knowledge to break them down into simple predictions tasks that can be performed with ML

    • "ML has the potential to become a cloud computing commodity. In contrast, the domain knowledge necessary to combine ML components into an end-to-end AI solution will not be commoditized. Those who have expertise that can break complex human business problems into ML-solvable components will succeed in building the next generation of business AI." (292)

  • Contemporary AI is driven by General-Purpose Machine Learning, some key components of which include deep neural nets, OOS validation, stochastic gradient descent for parameter optimization, and GPU hardware for parallelization
  • Deep Learning or Deep Neural Nets (DNNs) combine restrictive dimension reduction (like parametric models) with flexible function approximation (like nonparametric models) using many layers

    • Neural networks have a long history (including failed experiments with wide neural networks in the 1990s), but deep neural nets have been enabled recently by big data and GPUs

    • DNNs are modular: each layer plays a role and they can be swapped out, including to transfer learning between models

    • See Deep Learning by Goodfellow, Bengio, and Courville; Neural Networks and Deep Learning by Michael Nielsen

  • Stochastic Gradient Descent replaces the actual gradients with estimates of those gradients based on a subset of the data
  • Reinforcement Learning (RL) (aka active learning or sequential design of experiments) algorithms choose data consumed to continue learning

Errata

  • 37: "is then available via Bayes rule" --> "is then available via Bayes' rule"
  • 78: "in some data-dependent matter" --> "in some data-dependent manner"
  • 116: "We can then call cv.gamlr" --> "We can then call cv.glmnet"
  • 135: "it has increased from 0.055 to 0.64" --> "it has increased from 0.055 to 0.064"
  • 211: "repeatedly fitting regression" --> "repeatedly fitting a regression"
  • 222: "This show makes me feelfeel...." --> "This show makes me feel...."
  • 222: "I find this showfeel...." --> "I find this show...."
  • 237: "This data originally appear in" --> "These data originally appear in" or "This data originally appears in"

Created: 2021-04-16
Updated: 2021-11-21

Please drop me a note to share your thoughts or if you have a book to recommend: m.kudija@gmail.com