C++实现预测与分类评估与提升：理论与算法详解

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《评估与改进预测与分类：C++理论与算法》是一本由Timothy Masters编著的专业书籍，于2017年出版。该书专注于在信息技术领域中评估和优化预测和分类模型的理论和实践方法，尤其强调在C++编程环境中应用这些技术。作者通过深入探讨以下几个关键主题来帮助读者提升预测和分类任务的准确性： 1. **计算熵及问题检测**：书中介绍如何利用熵这一信息论工具来识别数据集中的潜在问题特征（即预测器），这些特征可能对模型的性能产生负面影响。通过测量不确定性，可以快速筛查出具有高预测潜力的候选特征。 2. **数值预测的改进**：作者提供了多种技术，如约束和非约束组合、方差加权插值以及核回归平滑，以提高数值预测的精度。这些方法旨在减小噪声影响，提升预测的稳健性。 3. **分类决策策略**：书中列举了多种分类决策规则，如Borda计数法、MinMax和MaxMin规则、并集和交集规则、逻辑回归、局部准确度选择、模糊积分最大化，以及配对耦合等，以便根据具体场景选择最合适的决策准则。 4. **信息论筛选**：作者利用信息论方法，如Shannon熵，对大量候选预测器进行高效筛选，帮助用户识别那些对预测结果影响最大的特征。 5. **随机检验方法**：通过蒙特卡洛重新排列（permutation testing）来评估模型性能中的随机成分，了解模型成功是否得益于运气，这对于理解模型的稳定性和可靠性至关重要。 6. **预测和分类的置信区间**：书中还讲解如何计算预测值的置信和容忍区间，以及分类决策的置信水平，这对于理解和解释模型的预测能力提供了量化依据。《评估与改进预测与分类：C++理论与算法》这本书不仅涵盖了理论基础，还提供了实用的编程技巧和实例，适合IT专业人士和机器学习爱好者深入学习和实践预测与分类技术。通过阅读和应用书中的内容，读者能够提升模型的性能，降低误差，并在实际项目中取得更好的结果。

• Many applications involve wildly throwing spaghetti on the wall to

see what sticks. A researcher may have literally hundreds or even

thousands of candidates for predictor variables, while the nal

model will employ only a handful. Computations involving mutual

information and uncertainty reduction between the candidates

and the predicted variable provide methods for rapidly screening

candidates, eliminating those that are least likely to be useful while

simultaneously discovering those that are most promising.

• One exciting subject in information theory is causation, the literal

effect of one event causing another, as opposed to their just being

related. Transfer entropy (Schreiber’s information transfer) quantifies

causative events.

These and many more topics are addressed in this text. Intuitive justification is a

focal point in every presentation. The goal is that you understand the problem and

the solution on a solid gut level. Then, one or more references are given as needed if

you want to see rigorous mathematical details. In most cases, only the equations that

are critical to the technique are provided here. Long and tedious proofs are invariably

left to the references. Finally, the technique is illustrated with heavily commented C++

source code. All code is supplied on my web site (TimothyMasters.info) as complete working

programs that can be compiled with the Microsoft Visual Studio compiler. Those

sections of code that are central to a technique are printed in the book for the purpose of

explication.

The ultimate purpose of this text is threefold. The first goal is to open the eyes of

serious developers to some of the hidden pitfalls that lurk in the model development

process. The second is to provide broad exposure for some of the most powerful model

enhancement algorithms that have emerged from academia in the past two decades,

while not bogging you down in cryptic mathematical theory. Finally, this text should

provide you with a toolbox of ready-to-use C++ code that can be easily incorporated into

your existing programs. Enjoy.

PrefaCe

dangerous if not done carefully. Ultimately, the choice of a numeric or classification

model depends on the nature of the data and on a sometimes arbitrary decision by

the experimenter. This chapter discusses methods for assessing models that make

numeric predictions.

Notation

Numeric prediction models use one or more independent variables to predict one or

more dependent variables. By common convention, the independent variables employed

by a model are designated by some form of the letter x, while the dependent variables

are designated by the letter y. Unless otherwise stated, scalar variables are represented in

lowercase italic type with an optional subscript, and vectors are represented in lowercase

bold type. Thus, we may refer to the vector x={x

, x

, …}. When we want to associate

x with a particular case in a collection, we may use a subscript as in x

. Matrices are

represented by uppercase bold type, such as X.

The parameters of a prediction model are Greek letters, with theta (θ) being

commonly employed. If the model has more than one parameter, separate Greek letters

may be used, or a single bold type vector (θ) may represent all of the parameters.

A model is often named after the variable it predicts. For example, suppose we

have a one-parameter model that uses a vector of independent variables to predict a

scalar variable. This model (or its prediction, according to context) would be referred

to as y(x; θ).

A collection of observed cases called the training set is used to optimize the

prediction model in some way, and then another independent collection of cases called

the test set or validation set is used to test the trained model. (Some schemes employ

three independent collections, using both a test set and a validation set. One is used

during model development, and the other is used for final verification. We’ll discuss

this later.) The error associated with case i in one of these collections is the difference

between the predicted and the observed values of the dependent variable. This is

expressed in Equation (1.1).

ey y

iii

()

-x ; q

(1.1)

Chapter 1 assessment ofnumeriC prediCtions

Overview of Performance Measures

There are at least three reasons why we need an effective way to measure the

performance of a model. The most obvious reason is that we simply need to know if

it is doing its job satisfactorily. If a model’s measured performance on its training set

is unsatisfactory, there is no point in testing it on an independent dataset; the model

needs revision. If the model performs well on the training set but performs poorly on

the independent set, we need to find out why and remedy the situation. Finally, if the

performance of a model is good when it is first placed in service but begins to deteriorate

as time passes, we need to discover this situation before damage is done.

The second reason for needing an effective performance criterion is that we must

have an objective criterion by which the suitability of trial parameter values may

be judged during training. The usual training procedure is to have an optimization

algorithm test many values of the model’s parameter (scalar or vector). For each trial

parameter, the model’s performance on the training set is assessed. The optimization

algorithm will select the parameter that provides optimal performance in the training

set. It should be apparent that the choice of performance criterion can have a

profound impact on the value of the optimal parameter that ultimately results from the

optimization.

The final reason for needing an effective performance criterion is subtle but

extremely important in many situations. When we compute the parameter value that

optimizes a performance criterion or when we use a performance criterion to choose the

best of several competing models, it is a little known fact that the choice of criterion can

have a profound impact on how well the model generalizes to cases outside the training

set. Obviously, a model that performs excellently on the training set but fails on new

cases is worthless. To encourage generalization ability, we need more than simply good

average performance on the training cases. We need consistency across the cases.

In other words, suppose we have two alternative performance criteria. We optimize

the model using the first criterion and find that the average performance in the training

set is quite good, but there are a few training cases for which the trained model performs

poorly. Alternatively, we optimize the model using the second criterion and find that the

average performance is slightly inferior to that of the first criterion, but all of the training

cases fare about equally well on the model. Despite the inferior average performance,

the model trained with the second criterion will almost certainly perform better than the

first when it is placed into service.

Chapter 1 assessment ofnumeriC prediCtions

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