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#003A Logistic Regression – Cost Function Optimization - Master Data Science


First, to train parameters \(w \) and \(b \) of a logistic regression model we need to define a cost function. Given a training set of \(m\) training examples, we want to find parameters \(w\) and \(b \), so that \(\hat{y}\) is as close to \(y \) (ground truth). Here, we will use \((i) \) superscript to index different training examples. Henceforth, we will use loss (error) function \(\mathcal{L}\) to measure how well our algorithm is doing. In logistic regression squared error loss function is not an optimal choice.

Bias: Friend or Foe? User Acceptance of Gender Stereotypes in Automated Career Recommendations Artificial Intelligence

Currently, there is a surge of interest in fair Artificial Intelligence (AI) and Machine Learning (ML) research which aims to mitigate discriminatory bias in AI algorithms, e.g. along lines of gender, age, and race. While most research in this domain focuses on developing fair AI algorithms, in this work, we show that a fair AI algorithm on its own may be insufficient to achieve its intended results in the real world. Using career recommendation as a case study, we build a fair AI career recommender by employing gender debiasing machine learning techniques. Our offline evaluation showed that the debiased recommender makes fairer career recommendations without sacrificing its accuracy. Nevertheless, an online user study of more than 200 college students revealed that participants on average prefer the original biased system over the debiased system. Specifically, we found that perceived gender disparity is a determining factor for the acceptance of a recommendation. In other words, our results demonstrate we cannot fully address the gender bias issue in AI recommendations without addressing the gender bias in humans.

Concept Drift Monitoring and Diagnostics of Supervised Learning Models via Score Vectors Machine Learning

Supervised learning models are one of the most fundamental classes of models. Viewing supervised learning from a probabilistic perspective, the set of training data to which the model is fitted is usually assumed to follow a stationary distribution. However, this stationarity assumption is often violated in a phenomenon called concept drift, which refers to changes over time in the predictive relationship between covariates $\mathbf{X}$ and a response variable $Y$ and can render trained models suboptimal or obsolete. We develop a comprehensive and computationally efficient framework for detecting, monitoring, and diagnosing concept drift. Specifically, we monitor the Fisher score vector, defined as the gradient of the log-likelihood for the fitted model, using a form of multivariate exponentially weighted moving average, which monitors for general changes in the mean of a random vector. In spite of the substantial performance advantages that we demonstrate over popular error-based methods, a score-based approach has not been previously considered for concept drift monitoring. Advantages of the proposed score-based framework include applicability to any parametric model, more powerful detection of changes as shown in theory and experiments, and inherent diagnostic capabilities for helping to identify the nature of the changes.

Feature space approximation for kernel-based supervised learning Machine Learning

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage consumption and computational complexity. Furthermore, the method can be regarded as a regularization technique, which improves the generalizability of learned target functions. We demonstrate significant improvements in comparison to the computation of data-driven predictions involving the full training data set. The method is applied to classification and regression problems from different application areas such as image recognition, system identification, and oceanographic time series analysis.

NeuCrowd: Neural Sampling Network for Representation Learning with Crowdsourced Labels Artificial Intelligence

Representation learning approaches require a massive amount of discriminative training data, which is unavailable in many scenarios, such as healthcare, small city, education, etc. In practice, people refer to crowdsourcing to get annotated labels. However, due to issues like data privacy, budget limitation, shortage of domain-specific annotators, the number of crowdsourced labels are still very limited. Moreover, because of annotators' diverse expertises, crowdsourced labels are often inconsistent. Thus, directly applying existing representation learning algorithms may easily get the overfitting problem and yield suboptimal solutions. In this paper, we propose \emph{NeuCrowd}, a unified framework for representation learning from crowdsourced labels. The proposed framework (1) creates a sufficient number of high-quality \emph{n}-tuplet training samples by utilizing safety-aware sampling and robust anchor generation; and (2) automatically learns a neural sampling network that adaptively learns to select effective samples for representation learning network. The proposed framework is evaluated on both synthetic and real-world data sets. The results show that our approach outperforms a wide range of state-of-the-art baselines in terms of prediction accuracy and AUC\footnote{To encourage the reproducible results, we make our code public on a github repository, i.e., \url{}}.

Structured Learning via Logistic Regression

Neural Information Processing Systems

A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through the addition of entropy terms, for fixed messages, the learning objective reduces to a traditional (non-structured) logistic regression problem with respect to parameters. In these logistic regression problems, each training example has a bias term determined by the current set of messages. Based on this insight, the structured energy function can be extended from linear factors to any function class where an "oracle" exists to minimize a logistic loss. Papers published at the Neural Information Processing Systems Conference.

A survey on Machine Learning-based Performance Improvement of Wireless Networks: PHY, MAC and Network layer Machine Learning

This paper provides a systematic and comprehensive survey that reviews the latest research efforts focused on machine learning (ML) based performance improvement of wireless networks, while considering all layers of the protocol stack (PHY, MAC and network). First, the related work and paper contributions are discussed, followed by providing the necessary background on data-driven approaches and machine learning for non-machine learning experts to understand all discussed techniques. Then, a comprehensive review is presented on works employing ML-based approaches to optimize the wireless communication parameters settings to achieve improved network quality-of-service (QoS) and quality-of-experience (QoE). We first categorize these works into: radio analysis, MAC analysis and network prediction approaches, followed by subcategories within each. Finally, open challenges and broader perspectives are discussed.

Large-scale Kernel Methods and Applications to Lifelong Robot Learning Machine Learning

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning algorithms to work with large amounts of data has become a crucial scientific and technological challenge for their practical applicability. Hence, it is no surprise that large-scale learning is currently drawing plenty of research effort in the machine learning research community. In this thesis, we focus on kernel methods, a theoretically sound and effective class of learning algorithms yielding nonparametric estimators. Kernel methods, in their classical formulations, are accurate and efficient on datasets of limited size, but do not scale up in a cost-effective manner. Recent research has shown that approximate learning algorithms, for instance random subsampling methods like Nystr\"om and random features, with time-memory-accuracy trade-off mechanisms are more scalable alternatives. In this thesis, we provide analyses of the generalization properties and computational requirements of several types of such approximation schemes. In particular, we expose the tight relationship between statistics and computations, with the goal of tailoring the accuracy of the learning process to the available computational resources. Our results are supported by experimental evidence on large-scale datasets and numerical simulations. We also study how large-scale learning can be applied to enable accurate, efficient, and reactive lifelong learning for robotics. In particular, we propose algorithms allowing robots to learn continuously from experience and adapt to changes in their operational environment. The proposed methods are validated on the iCub humanoid robot in addition to other benchmarks.

An Empirical and Comparative Analysis of Data Valuation with Scalable Algorithms Machine Learning

This paper focuses on valuating training data for supervised learning tasks and studies the Shapley value, a data value notion originated in cooperative game theory. The Shapley value defines a unique value distribution scheme that satisfies a set of appealing properties desired by a data value notion. However, the Shapley value requires exponential complexity to calculate exactly. Existing approximation algorithms, although achieving great improvement over the exact algorithm, relies on retraining models for multiple times, thus remaining limited when applied to larger-scale learning tasks and real-world datasets. In this work, we develop a simple and efficient heuristic for data valuation based on the Shapley value with complexity independent with the model size. The key idea is to approximate the model via a $K$-nearest neighbor ($K$NN) classifier, which has a locality structure that can lead to efficient Shapley value calculation. We evaluate the utility of the values produced by the $K$NN proxies in various settings, including label noise correction, watermark detection, data summarization, active data acquisition, and domain adaption. Extensive experiments demonstrate that our algorithm achieves at least comparable utility to the values produced by existing algorithms while significant efficiency improvement. Moreover, we theoretically analyze the Shapley value and justify its advantage over the leave-one-out error as a data value measure.

The impact of imbalanced training data on machine learning for author name disambiguation Machine Learning

In supervised machine learning for author name disambiguation, negative training data are often dominantly larger than positive training data. This paper examines how the ratios of negative to positive training data can affect the performance of machine learning algorithms to disambiguate author names in bibliographic records. On multiple labeled datasets, three classifiers - Logistic Regression, Na\"ive Bayes, and Random Forest - are trained through representative features such as coauthor names, and title words extracted from the same training data but with various positive-negative training data ratios. Results show that increasing negative training data can improve disambiguation performance but with a few percent of performance gains and sometimes degrade it. Logistic Regression and Na\"ive Bayes learn optimal disambiguation models even with a base ratio (1:1) of positive and negative training data. Also, the performance improvement by Random Forest tends to quickly saturate roughly after 1:10 ~ 1:15. These findings imply that contrary to the common practice using all training data, name disambiguation algorithms can be trained using part of negative training data without degrading much disambiguation performance while increasing computational efficiency. This study calls for more attention from author name disambiguation scholars to methods for machine learning from imbalanced data.