A Note on High-Probability versus In-Expectation Guarantees of Generalization Bounds in Machine Learning

Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample that is not representative of the underlying distribution, one cannot expect to construct a reliable machine learning model. Following that, statements made about the performance of machine learning models have to take the sampling process into account. The two common approaches for that are to generate statements that hold either in high-probability, or in-expectation, over the random sampling process. In this short note we show how one may transform one statement to another. As a technical novelty we address the case of unbounded loss function, where we use a fairly new assumption, called the witness condition

Semi-Supervised Learning, Causality and the Conditional Cluster Assumption

While the success of semi-supervised learning (SSL) is still not fully understood, Sch\"olkopf et al. (2012) have established a link to the principle of independent causal mechanisms. They conclude that SSL should be impossible when predicting a target variable from its causes, but possible when predicting it from its effects. Since both these cases are somewhat restrictive, we extend their work by considering classification using cause and effect features at the same time, such as predicting disease from both risk factors and symptoms. While standard SSL exploits information contained in the marginal distribution of all inputs (to improve the estimate of the conditional distribution of the target given inputs), we argue that in our more general setting we should use information in the conditional distribution of effect features given causal features. We explore how this insight generalises the previous understanding, and how it relates to and can be exploited algorithmically for SSL.Comment: 36th Conference on Uncertainty in Artificial Intelligence (2020) (Previously presented at the NeurIPS 2019 workshop "Do the right thing": machine learning and causal inference for improved decision making, Vancouver, Canada.

A Brief Prehistory of Double Descent

In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a function of some (approximate) measure of its complexity $N$. With $N$ the number of features, these curves are also referred to as feature curves. A salient observation in [1] is that these curves can display, what they call, double descent: with increasing $N$, the risk initially decreases, attains a minimum, and then increases until $N$ equals $n$, where the training data is fitted perfectly. Increasing $N$ even further, the risk decreases a second and final time, creating a peak at $N=n$. This twofold descent may come as a surprise, but as opposed to what [1] reports, it has not been overlooked historically. Our letter draws attention to some original, earlier findings, of interest to contemporary machine learning

The Determinants of Good Newborn Care Practices in the Rural Areas of Nepal.

Newborn morbidity and mortality remains high despite a remarkable decline in the infant mortality and under five mortality rates in Nepal over the last decade (1996-2006). Research shows that newborns’ health outcome is associated with maternal and other factors. This study was designed to understand the factors that have an impact on three good newborn care practices: safe cord cutting, early breastfeeding and delayed bathing. The study used the interview data of 815 married women aged 15-49 years who delivered a live baby between February 2008 and February 2009, collected for the baseline survey of the Community-Based Maternal and Newborn Health program implemented in the Sindhuli district of Nepal. The mean age of the sample women was 26 years. Two-thirds of them were from disadvantaged indigenous caste/ethnicity groups, about 70% were uneducated and the majority were poor. Safe cord cutting, early breastfeeding and delayed bathing practices were studied for 803, 810 and 812 women respectively and 70.7%, 46.7%, and 16.6% of the eligible samples demonstrated the practices respectively. The logistic regression method was used to examine the association of independent factors with the outcome variables. Social gradient was found to be associated with all three practices. Rich women were more likely to demonstrate good practices and bearing a child at the prime age (20-34 years) was likely to result in safe cord cutting. Disadvantaged indigenous and ‘other’ caste/ethnicity women demonstrated unsafe cord cutting practices and dalit caste/ethnicity women demonstrated poor bathing practices. Maternal knowledge also emerged as a strong predictor of early breastfeeding and delayed bathing practices. Antenatal care from a SBA determined good breastfeeding and advice from a FCHV determined good bathing practices. The results showed that the uptake of antenatal and delivery services from a skilled birth attendant is unacceptably low in rural Nepal, which is a challenge for meeting the millennium development goals. The study recommends programmes for improving economic status as a key to improving newborn care practices. As the vast majority of the deliveries are still assisted by traditional birth attendants; including them in maternal health programmes is crucial. Increasing women’s access to a skilled birth attendant and boosting the spirit of the FCHVs to increase their efficiency is also recommended. Future research on newborn health should focus on identifying other determinants of newborn care practices and survival. Qualitative studies to understand the cultural perspectives of newborn care practices are also recommended