Parametric PDF for Goodness of Fit Natan Katz natan.katzgmail.comUri Utai

2025-05-02 0 0 726.63KB 14 页 10玖币

侵权投诉

Parametric PDF for Goodness of Fit

Natan Katz

natan.katz@gmail.com

Uri Utai

uri.itai@gmail.com

October 2022

Abstract

The methods for the goodness of ﬁt in classiﬁcation problems require

a prior threshold for determining the confusion matrix. Nonetheless, this

ﬁxed threshold removes information that the model’s curves provide, and

can be used, for further studies such as risk evaluation and stability analy-

sis. We present a diﬀerent framework that allows us to perform this study

using a parametric PDF.

1 Introduction

Machine learning (ML) projects have become a leading tool in enormous do-

mains of the computer industry. Their rule is far beyond computational as-

pects. Indeed, they are a focal point in designing analytical business decisions.

The commercial usage of these models raises new challenges. The ML academic

research often assumes that :

•The data in the database represents well the global data distribution.

•Training methodology aligns with the model’s KPI.

•There are no production-driven drawbacks.

Unfortunately, none of these assumptions hold in real-world models. In addi-

tion, cardinal issues that focus on complexity and stability and questions such

as ”what is the eﬃcient way to set a threshold to have both good

and stable performance” rarely exist in the academy. Hence, deploying ML

models in the real world requires a methodology that the academy does not

provide. In the academy, researchers focus mainly on common KPIs such as

accuracy and precision. We use these KPIs for other scaling indicators such as

Creamer’s V, F1-score, AUC [Uri22] and Matthew correlation coeﬃcient (MCC)

[CJ20; JRF12; AD54; Uri22]. These indicators require a prior threshold for us-

ing them. Thus they all act as discrete signals . In the following sections, we

discuss the derived drawbacks of discrete signals and suggest solutions.

arXiv:2210.14005v2 [cs.LG] 1 Nov 2022

2 Discrete Signals

In this section, we discuss the disadvantages of discrete signals. To do so, we

need to review the typical inference process.

2.1 Inference Overview

Consider a well trained model Mand an evaluation set Dtest one can eas-

ily deduce fromﬁg 1 that the confusion matrix fully determines the model’s

evaluation. It leads to the following deﬁnition.

Deﬁnition: [Discrete signal] Let Mbe the confusion matrix. Consider the func-

tion

F:M→R

If Fis monotone for each entry of M, then F is a Discrete signal.

If Fdoes not depend on Mthen it is called Continuous signals. We note

that the domain on the Discrete signal can be every nonempty subset of the

entries of M.

The output of a classiﬁcation model is a probabilities vector [pyt16; skl]. We

use these vectors to calculate FR and TR curves. For classifying the data, we

set a threshold. This threshold determines the confusion matrix. This matrix

is the domain of the discrete signals [Uri22]. Most of the common goodness of

ﬁt KPIs are discrete signals, nonetheless, these signals may suﬀer from three

essential disadvantages:

•Unstable concerning the threshold

•Diﬃcult for risk calculations

•Absence of good mathematical toolbox

In the following subsections, we discuss these disadvantages.

2.2 Instability

Model’s performances have a substantial capital impact. Therefore it is crucial

to evaluate our indicators accurately. Setting a ﬁxed threshold on the model

graphs may provide two caveats:

•Typical graphs suﬀer from steep slopes concerning the thresholds

•Real-world statistics do not always identical to the distribution of the

evaluation test

Academically, these phenomena are seldom studied. Nonetheless, diﬀerent dis-

tributions and steep slopes often indicate instability. Thus, we ﬁnd these caveats

cardinal in the commercial world.

Figure 1: Generic Inference Process

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

ParametricPDFforGoodnessofFitNatanKatznatan.katz@gmail.comUriUtaiuri.itai@gmail.comOctober2022AbstractThemethodsforthegoodnessoftinclassicationproblemsrequireapriorthresholdfordeterminingtheconfusionmatrix.Nonetheless,thisxedthresholdremovesinformationthatthemodel'scurvesprovide,andcanbeused,forf...

展开>> 收起<<

Parametric PDF for Goodness of Fit Natan Katz natan.katzgmail.comUri Utai.pdf

共14页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Parametric PDF for Goodness of Fit Natan Katz natan.katzgmail.comUri Utai

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: