机器学习：模式、预测与行动

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"《Patterns, Predictions, and Actions》是由Moritz Hardt和Benjamin Recht合著的一本关于机器学习的书籍，旨在探讨模式识别、预测与行动在机器学习中的角色。书中深入浅出地介绍了20世纪的雄心壮志、模式分类、决策制定、监督学习以及表示和特征等核心概念，并对优化方法进行了讨论。这本书是作者的工作草稿，不断更新，可在https://mlstory.org获取最新版本。" 正文：本书首先介绍了20世纪的科学雄心，尤其是在模式分类方面的进展。模式分类是机器学习的基础，它涉及识别数据中的模式并利用这些模式进行预测。作者详细解释了如何通过算法来实现这一目标，例如感知机（Perceptron），这是一种早期的学习算法，用于处理二元分类问题。接着，书中深入讨论了预测与行动的关系，这是机器学习中决策制定的关键环节。他们引入了贝叶斯二项假设测试，这是一个评估模型假设的有效工具。通过分析似然比测试的典型情况，书中阐述了错误类型和成功标准，并引用了奈曼-皮尔逊引理，进一步理解了接收者操作特性（ROC）曲线的性质。当模型未知时，如何做出有效决策也是讨论的重点。监督学习是机器学习的一个主要分支，书中解释了样本与总体的区别，并定义了监督学习的概念。作者通过介绍感知机算法，展示了如何通过迭代更新权重来逐步改进模型的预测能力。在表示和特征部分，作者强调了测量和量化的重要性，这些都是构建有效预测模型的基础。他们探讨了模板匹配、数据的总结与直方图，以及非线性预测器的角色，揭示了特征选择和预处理在提升模型性能上的关键作用。最后，书中触及了优化主题，这是机器学习算法实现的核心。基本的优化原理如梯度下降被详尽阐述，包括其工作原理和在实际问题中的应用。这部分内容为读者提供了深入理解模型训练过程的窗口。《Patterns, Predictions, and Actions》是一本涵盖了机器学习基础和进阶概念的综合读物，适合对这一领域有浓厚兴趣的读者。书中通过实例和理论相结合的方式，帮助读者理解并掌握机器学习的关键技术。

16 patterns, predictions, and actions

was so successful, in fact, that it became the new artiﬁcial intelligence

in the public narrative of popular media. The technology reached

entirely new levels of commercial signiﬁcance with companies com-

peting ﬁercely over advances in the space.

This new artiﬁcial intelligence had done away with the sym-

bolic reasoning of the McCarthy era. Instead, the central drivers of

progress were widely regarded as growing datasets, increasing com-

pute resources, and more benchmarks along with publicly available

code to start from. Are those then the only ingredients needed to

secure the sustained success of machine learning in the real world?

Prediction and action

Unknown outcomes often follow patterns found in past observations.

But what do we do with the patterns we ﬁnd and the predictions

we make? Like Halley proposing his life table for annuity pricing,

predictions only become useful when they are acted upon. But going

from patterns and predictions to successful actions is a delicate task.

How can we even anticipate the effect of a hypothetical action when

our actions now inﬂuence the data we observe and value we accrue

in the future?

One way to determine the effect of an action is experimentation:

try it out and see what happens. But there’s a lot more we can do

if we can model the situation more carefully. A model of the envi-

ronment speciﬁes how an action changes the state of the world, and

how in turn this state results in a gain or loss of utility. We include

some aspects of the environment explicitly as variables in our model.

Others we declare exogenous and model as noise in our system.

The solution of how to take such models and turn them into plans

of actions that maximize expected utility is a mathematical achieve-

ment of the 20th century. By and large, such problems can be solved

by dynamic programming. Initially formulated by Bellman in 1954,

dynamic programming poses optimization problems where at ev-

ery time step, we observe data, take an action, and pay a cost. By

chaining these together in time, elaborate plans can be made that

remain optimal under considerable stochastic uncertainty. These

ideas revolutionized aerospace in the 1960s, and are still deployed

in infrastructure planning, supply chain management, and the land-

ing of SpaceX rockets. Dynamic programming remains one of the

most important algorithmic building blocks in the computer science

toolkit.

Planning actions under uncertainty has also always been core to

artiﬁcial intelligence research, though initial proposals for sequential

decision making in AI were more inspired by neuroscience than oper-

introduction 17

ations research. In 1950-era AI, the main motivating concept was one

of reinforcement learning, which posited that one should encourage

taking actions that were successful in the past. This reinforcement

strategy led to impressive game-playing algorithms like Samuel’s

Checkers Agent circa 1959. Surprisingly, it wasn’t until the 1990s

that researchers realized that reinforcement learning methods were

approximation schemes for dynamic programming. Powered by this

connection, a mix of researchers from AI and operations research

applied neural nets and function approximation to simplify the ap-

proximate solution of dynamic programming programming problems.

The subsequent 30 years have led to impressive advances in reinforce-

ment learning and approximate dynamic programming techniques

culminating in solving the game of Go and in powering dexterous

manipulation in robotic systems.

Central to the reinforcement learning paradigm is understanding

how to balance learning about an environment and acting on it. This

balance is a non-trivial problem even in the case where actions do

not lead to a change in state. In the context of machine learning,

experimentation in the form of taking an action and observing its

effect often goes by the name exploration. Exploration reveals the

payoff of an action, but it comes at the expense of not taking an

action that we already knew had a decent payoff. Thus, there is an

inherent tradeoff between exploration and exploitation of previous

actions. Though in theory, the optimal balance can be computed by

dynamic programming, it is more common to employ techniques

from bandit optimization that are simple and effective strategies to

balance exploration and exploitation.

Not limited to experimentation, causality is a comprehensive

conceptual framework to reason about the effect of actions. Causal

inference, in principle, allows us to estimate the effect of hypothetical

actions from observational data. A growing technical repertoire of

causal inference is taking various sciences by storm as witnessed

in epidemiology, political science, policy, climate, and development

economics.

There are good reasons that many see causality as a promising

avenue for making machine learning methods more robust and reli-

able. Current state-of-the-art predictive models remain surprisingly

fragile to changes in the data. Even small natural variations in a data-

generating process can signiﬁcantly deteriorate performance. There

is hope that tools from causality could lead to machine learning

methods that perform better under changing conditions.

However, causal inference is no panacea. There are no causal

insights without making substantive judgments about the problem

that are not veriﬁable from data alone. The reliance on hard earned

18 patterns, predictions, and actions

substantive domain knowledge stands in contrast with the nature of

recent advances in machine learning that largely did without—and

that was the point.

About this book

This is a book for all students in the sprawling ﬁeld of machine

learning. The material we cover supports a one semester graduate

introduction to machine learning. We invite readers from all back-

grounds; some experience with probability, calculus, and linear

algebra sufﬁces.

In its conception, our book is both an old take on something new

and a new take on something old.

Looking at it one way, we return to the roots with our emphasis

on pattern classiﬁcation. We believe that the practice of machine

learning today is surprisingly similar to pattern classiﬁcation of the

1960s, with a few notable innovations from more recent decades.

This is not to understate recent progress. Like many, we are

amazed by the advances that have happened in recent years. Im-

age recognition has improved dramatically. Even small devices can

now reliably recognize speech. Natural language processing and

machine translation have made massive leaps forward. Machine

learning has even been helpful in some difﬁcult scientiﬁc problems,

such as protein folding.

However, we think that it would be a mistake not to recognize

pattern classiﬁcation as a driving force behind these improvements.

The ingenuity behind many advances in machine learning so far lies

not in a fundamental departure from pattern classiﬁcation, but rather

in ﬁnding new ways to make problems amenable to the model ﬁtting

techniques of pattern classiﬁcation.

Consequently, the ﬁrst few chapters of this book follow relatively

closely the excellent text “Pattern Classiﬁcation and Scene Analysis”

by Duda and Hart, particularly, its ﬁrst edition from 1973, which

remains relevant today. Indeed, Duda and Hart summarize the state

of pattern classiﬁcation in 1973, and it bears a striking resemblance to

the core of what we consider today to be machine learning. We add

new developments on representations, optimization, and generaliza-

tion, all of which remain topics of evolving, active research.

Looking at it differently, our book departs in some considerable

ways from the way machine learning is commonly taught.

First, our text emphasizes the role that datasets play in machine

learning. A full chapter explores the histories, signiﬁcance, and scien-

tiﬁc basis of machine learning benchmarks. Although ubiquitous and

taken for granted today, the datasets-as-benchmarks paradigm was

introduction 19

a relatively recent development of the 1980s. Detailed consideration

of datasets, the collection and construction of data, as well as the

training and testing paradigm, tend to be lacking from theoretical

courses on machine learning.

Second, the book includes a modern introduction to causality and

the practice of causal inference that lays to rest dated controversies in

the ﬁeld. The introduction is self-contained, starts from ﬁrst princi-

ples, and requires no prior commitment intellectually or ideologically

to the ﬁeld of causality. Our treatment of causality includes the con-

ceptual foundations, as well as some of the practical tools of causal

inference increasingly applied in numerous applications. It’s interest-

ing to note that many recent causal estimators reduce the problem of

causal inference in clever ways to pattern classiﬁcation. Hence, this

material ﬁts quite well with the rest of the book.

Third, our book covers sequential and dynamic models thoroughly.

Though such material could easily ﬁll a semester course on its own,

we wanted to provide the basic elements required to think about

making decisions in dynamic contexts. In particular, given so much

recent interest in reinforcement learning, we hope to provide a self-

contained short introduction to the concepts underpinning this ﬁeld.

Our approach here follows our approach to supervised learning: we

focus on how we would make decisions given a probabilistic model

of our environment, and then turn to how to take action when the

model is unknown. Hence, we begin with a focus on optimal se-

quential decision making and dynamic programming. We describe

some of the basic solution approaches to such problems, and discuss

some of the complications that arise as our measurement quality

deteriorates. We then turn to making decisions when our models

are unknown, providing a survey of bandit optimization and rein-

forcement learning. Our focus here is to again highlight the power

of prediction. We show that for most problems, pattern recognition

can be seen as a complement to feedback control, and we highlight

how “certainty equivalent” decision making—where we ﬁrst use data

to estimate a model and then use feedback control acting as if this

model were true—is optimal or near optimal in a surprising number

of scenarios.

Finally, we attempt to highlight in a few different places through-

out the potential harms, limitations, and social consequences of

machine learning. From its roots in World War II, machine learning

has always been political. Advances in artiﬁcial intelligence feed into

a global industrial military complex, and are funded by it. As useful

as machine learning is for some unequivocally positive applications

such as assistive devices, it is also used to great effect for tracking,

surveillance, and warfare. Commercially its most successful use cases

20 patterns, predictions, and actions

Bellhouse, “A New Look at Halley’s

Life Table,” Journal of the Royal Statistical

Society: Series A (Statistics in Society) 174,

no. 3 (2011): 823–32.

Ciecka, “Edmond Halley’s Life Table

and Its Uses,” J. Legal Econ. 15 (2008):

65.

Pearson and Pearson, “The History of

Statistics in the 17th and 18th Centuries

Against the Changing Background of

Intellectual, Scientiﬁc and Religious

Thought,” British Journal for the Philoso-

phy of Science 32, no. 2 (1981): 177–83.

to date are targeted advertising and digital content recommendation,

both of questionable value to society. Several scholars have explained

how the use of machine learning can perpetuate inequity through

the ways that it can put additional burden on already marginalized,

oppressed, and disadvantaged communities. Narratives of artiﬁcial

intelligence also shape policy in several high stakes debates about the

replacement of human judgment in favor of statistical models in the

criminal justice system, health care, education, and social services.

There are some notable topics we left out. Some might ﬁnd that

the most glaring omission is the lack of material on unsupervised

learning. Indeed, there has been a signiﬁcant amount of work on

unsupervised learning in recent years. Thankfully, some of the most

successful approaches to learning without labels could be described

as reductions to pattern recognition. For example, researchers have

found ingenious ways of procuring labels from unlabeled data points,

an approach called self supervision. We believe that the contents of

this book will prepare students interested in these topics well.

In writing this book, our goal was to balance mathematical rigor

against presenting insights we have found useful in the most direct

way possible. In contemporary learning theory important results

often have short sketches, yet making these arguments rigorous and

precise may require dozens of pages of technical calculations. Such

proofs are critical to the community’s scientiﬁc activities but often

make important insights hard to access for those not yet versed in

the appropriate techniques. On the other hand, many machine learn-

ing courses drop proofs altogether, thereby losing the important

foundational ideas that they contain. We aim to strike a balance, in-

cluding full details for as many arguments as possible, but frequently

referring readers to the relevant literature for full details.

Chapter notes

Halley’s life table has been studied and discussed extensively; for

an entry point, see recent articles by Bellhouse

and Ciecka,

or the

article by Pearson and Pearson.

Halley was not the ﬁrst to create a life table. In fact, what Hal-

ley created is more accurately called a population table. Instead,

John Grount deserves credit for the ﬁrst life table in 1662 based on

mortality records from London. Considered to be the founder of de-

mography and an early epidemiologist, Grount’s work was in many

ways more detailed than Halley’s ﬂeeting engagement with Bres-

lau’s population. However, to Grount’s disadvantage the mortality

records released in London at the time did not include the age of the

deceased, thus complicating the work signiﬁcantly.

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