Logit | EPFL Graph Search

In statistics, the logit (ˈloʊdʒɪt ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function \sigma(x) = 1/(1+e^{-x}), so the logit is defined as :\operatorname{logit} p = \sigma^{-1}(p) = \ln \frac{p}{1-p} \quad \text{for} \quad p \in (0,1). Because of this, the logit is also called the log-odds since it is equal to the logarithm of the odds \frac{p}{1-p} where p is a probability. Thus, the logit is a type of function that maps probability values from (0, 1) to real numbers in (-\infty, +\infty), akin to the probit function. Definition If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the

Enhancing discrete choice models with representation learning

Alexandre Massoud Alahi, Virginie Janine Camille Lurkin, Brian Alan Sifringer

In discrete choice modeling (DCM), model misspecifications may lead to limited predictability and biased parameter estimates. In this paper, we propose a new approach for estimating choice models in which we divide the systematic part of the utility specification into (i) a knowledge-driven part, and (ii) a data-driven one, which learns a new representation from available explanatory variables. Our formulation increases the predictive power of standard DCM without sacrificing their interpretability. We show the effectiveness of our formulation by augmenting the utility specification of the Multinomial Logit (MNL) and the Nested Logit (NL) models with a new non linear representation arising from a Neural Network (NN), leading to new choice models referred to as the Learning Multinomial Logit (L-MNL) and Learning Nested Logit (L-NL) models. Using multiple publicly available datasets based on revealed and stated preferences, we show that our models outperform the traditional ones, both in terms of predictive performance and accuracy in parameter estimation. All source code of the models are shared to promote open science.

2020

On Certifying Non-Uniform Bounds against Adversarial Attacks

Volkan Cevher, Chen Liu

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to study the decision boundary of neural network models. We formulate our target as an optimization problem with nonlinear constraints. Then, a framework applicable for general feedforward neural networks is proposed to bound the output logits so that the relaxed problem can be solved by the augmented Lagrangian method. Our experiments show the non-uniform bounds have larger volumes than uniform ones and the geometric similarity of the non-uniform bounds gives a quantitative, dataagnostic metric of input features’ robustness. Further, compared with normal models, the robust models have even larger non-uniform bounds and better interpretability.

2019

Automatic Personality Perception

Gelareh Mohammadi

Whenever we meet a person for the first time, we tend to attribute personality traits to him/her. The process takes place in less than a second and it is spontaneous and unconscious. While not necessarily accurate (attributed traits do not necessarily correspond to the actual traits of the person), the process still influences significantly our behavior towards others, especially when it comes to social interactions. The phenomenon is so pervasive that it takes place not only when we meet others in person, but also when we observe them in video recordings or we simply interact with an artifact displaying human-like behaviors (robots, artificial agents, animated characters, etc.). This thesis focuses on one aspect of the phenomenon above, namely the spontaneous attribution of personality traits to speakers we never heard before. The prediction of traits attributed to others is important because it can help to better understand the social behavior of people. Furthermore, it can help to design artificial agents capable of eliciting the perception of predefined desirable traits. The experiments of the Thesis are performed over the Speaker Personality Corpus, a collection of 640 speech clips (322 identities in total) annotated in terms of personality traits by 11 assessors. The dataset was used not only for the experiments of this work, but also in an international benchmarking campaign (The Speaker Trait Challenge at INTERSPEECH 2012) allowing the comparison of several approaches proposed by different groups. The thesis includes two main achievements. The first is an approach capable of predicting whether a speaker is perceived to be in the upper or lower part of the observed scores along the Big-Five Traits, the personality dimensions known to capture most of the individual differences. The second is an approach for automatically ordering pairs of speakers along the Big Five Traits, a task that better fits the actual cognitive processes aimed at personality perception. The pairwise ranking scheme relies on an Ordinal Regression approach based on the Ordered Logit Model and on Gaussian Processes. A new, fully Bayesian approach was developed for inferring the parameters of the model.

EPFL2013

Automatic Personality Perception

Gelareh Mohammadi

EPFL2013