scholarly journals Neural Legal Outcome Prediction with Partial Least Squares Compression

Stats ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 396-411
Author(s):  
Charles Condevaux
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Outcome Prediction ◽  
Linear Models ◽  
Classification Problems ◽  
Common Goal ◽  
Multiclass Problem ◽  
European Court ◽  
Classification Tasks ◽  
Factual Data

Predicting the outcome of a case from a set of factual data is a common goal in legal knowledge discovery. In practice, solving this task is most of the time difficult due to the scarcity of labeled datasets. Additionally, processing long documents often leads to sparse data, which adds another layer of complexity. This paper presents a study focused on the french decisions of the European Court of Human Rights (ECtHR) for which we build various classification tasks. These tasks consist first of all in the prediction of the potential violation of an article of the convention, using extracted facts. A multiclass problem is also created, with the objective of determining whether an article is relevant to plead given some circumstances. We solve these tasks by comparing simple linear models to an attention-based neural network. We also take advantage of a modified partial least squares algorithm that we integrate in the aforementioned models, capable of effectively dealing with classification problems and scale with sparse inputs coming from natural language tasks.

Kernel Regularized Least Squares: Reducing Misspecification Bias with a Flexible and Interpretable Machine Learning Approach

2014 ◽  
Vol 22 (2) ◽  
pp. 143-168 ◽  
Author(s):  
Jens Hainmueller ◽  
Chad Hazlett
Keyword(s):  
Machine Learning ◽  
Social Science ◽  
Least Squares ◽  
Linear Models ◽  
Science Inquiry ◽  
Classification Problems ◽  
Regularized Least Squares ◽  
Inference Problems ◽  
Heterogeneous Effects ◽  
Best Fitting

We propose the use of Kernel Regularized Least Squares (KRLS) for social science modeling and inference problems. KRLS borrows from machine learning methods designed to solve regression and classification problems without relying on linearity or additivity assumptions. The method constructs a flexible hypothesis space that uses kernels as radial basis functions and finds the best-fitting surface in this space by minimizing a complexity-penalized least squares problem. We argue that the method is well-suited for social science inquiry because it avoids strong parametric assumptions, yet allows interpretation in ways analogous to generalized linear models while also permitting more complex interpretation to examine nonlinearities, interactions, and heterogeneous effects. We also extend the method in several directions to make it more effective for social inquiry, by (1) deriving estimators for the pointwise marginal effects and their variances, (2) establishing unbiasedness, consistency, and asymptotic normality of the KRLS estimator under fairly general conditions, (3) proposing a simple automated rule for choosing the kernel bandwidth, and (4) providing companion software. We illustrate the use of the method through simulations and empirical examples.

scholarly journals Nonlinear Partial Least Squares An Overview

2011 ◽  
pp. 169-189 ◽  
Author(s):  
Roman Rosipal
Keyword(s):  
Data Analysis ◽  
Least Squares ◽  
Partial Least Squares ◽  
Latent Variables ◽  
Linear Models ◽  
Simple Approximation ◽  
Computationally Efficient ◽  
Nonlinear Relation ◽  
Data Analytic ◽  
Pls Method

In many areas of research and industrial situations, including many data analytic problems in chemistry, a strong nonlinear relation between different sets of data may exist. While linear models may be a good simple approximation to these problems, when nonlinearity is severe they often perform unacceptably. The nonlinear partial least squares (PLS) method was developed in the area of chemical data analysis. A specific feature of PLS is that relations between sets of observed variables are modeled by means of latent variables usually not directly observed and measured. Since its introduction, two methodologically different concepts of fitting existing nonlinear relationships initiated development of a series of different nonlinear PLS models. General principles of the two concepts and representative models are reviewed in this chapter. The aim of the chapter is two-fold i) to clearly summarize achieved results and thus ii) to motivate development of new computationally efficient nonlinear PLS models with better performance and good interpretability.

An fMRI study examining spatial navigation through a virtual environment: Partial least squares analysis

2005 ◽  
Author(s):  
Richard Mraz ◽  
Nancy J. Lobaugh ◽  
Genevieve Quintin ◽  
Konstantine K. Kakzanis ◽  
Simon J. Graham
Keyword(s):  
Least Squares ◽  
Virtual Environment ◽  
Partial Least Squares ◽  
Spatial Navigation ◽  
Partial Least Squares Analysis ◽  
Fmri Study

Controlling in der Produktentwicklung

Controlling ◽  
2020 ◽  
Vol 32 (3) ◽  
pp. 45-50
Author(s):  
Marc Janka
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Finite Mixture

Gemeinhin gilt die Annahme, dass das Controlling für viele deutsche Unternehmen auch oder besonders in der Produktentwicklung von großer Bedeutung ist und vor allem unter Umfeldunsicherheit ein wesentlicher Erfolgsfaktor sein kann. Der vorliegende Beitrag zeigt unter Anwendung einer für die Controlling-Forschung neuartigen Methode zur Schätzung von Mischverteilungen mittels partieller Regressionen (englisch finite mixture partial least squares [FIMIX-PLS]), ob diese Annahme für alle Unternehmen gleichermaßen gilt.

Partial Least Squares Strukturgleichungsmodellierung

2017 ◽  
Author(s):  
Joseph F. Hair ◽  
Sven Hauff ◽  
G. Tomas M. Hult ◽  
Nicole F. Richter ◽  
Christian M. Ringle ◽  
...  
Keyword(s):  
Least Squares ◽  
Partial Least Squares

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

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