This paper considers the task of learning users' preferences on a combinatorial set of alternatives, as generally used by online configurators, for example. In many settings, only a set of selected alternatives during past interactions is available to the learner. Fargier et al. [2018] propose an approach to learn, in such a setting, a model of the users' preferences that ranks previously chosen alternatives as high as possible; and an algorithm to learn, in this setting, a particular model of preferences: lexicographic preferences trees (LP-trees). In this paper, we study complexity-theoretical problems related to this approach. We give an upper bound on the sample complexity of learning an LP-tree, which is logarithmic in the number of attributes. We also prove that computing the LP tree that minimises the empirical risk can be done in polynomial time when restricted to the class of linear LP-trees.

Machine learning is important because it gives enterprises a view of trends in customer behavior and business operational patterns, as well as supports the development of new products. Many of today's leading companies, such as Facebook, Google and Uber, make machine learning a central part of their operations. Machine learning has become a significant competitive differentiator for many companies. Classical machine learning is often categorized by how an algorithm learns to become more accurate in its predictions. There are four basic approaches: supervised learning, unsupervised learning, semi-supervised learning and reinforcement learning.

Every year, thousands of innocent people die due to heart attacks. Often undiagnosed heart attacks can hit people by surprise since many current medical plans don't cover the costs to require the searching of calcification on these scans. Only if someone is suspected to have a heart problem, a gated CT scan is taken, otherwise, there's no way for the patient to be aware of a possible heart attack/disease. While nongated CT scans are more periodically taken, it is harder to detect calcification and is usually taken for a purpose other than locating calcification in arteries. In fact, in real time coronary artery calcification scores are only calculated on gated CT scans, not nongated CT scans. After training a unet model on the Coronary Calcium and chest CT's gated scans, it received a DICE coefficient of 0.95 on its untouched test set. This model was used to predict on nongated CT scans, performing with a mean absolute error (MAE) of 674.19 and bucket classification accuracy of 41% (5 classes). Through the analysis of the images and the information stored in the images, mathematical equations were derived and used to automatically crop the images around the location of the heart. By performing semi-supervised learning the new cropped nongated scans were able to closely resemble gated CT scans, improving the performance by 91% in MAE (62.38) and 23% in accuracy.

Existing work on fairness typically focuses on making known machine learning algorithms fairer. Fair variants of classification, clustering, outlier detection and other styles of algorithms exist. However, an understudied area is the topic of auditing an algorithm's output to determine fairness. Existing work has explored the two group classification problem for binary protected status variables using standard definitions of statistical parity. Here we build upon the area of auditing by exploring the multi-group setting under more complex definitions of fairness.

Recently, vehicle similarity learning, also called re-identification (ReID), has attracted significant attention in computer vision. Several algorithms have been developed and obtained considerable success. However, most existing methods have unpleasant performance in the hazy scenario due to poor visibility. Though some strategies are possible to resolve this problem, they still have room to be improved due to the limited performance in real-world scenarios and the lack of real-world clear ground truth. Thus, to resolve this problem, inspired by CycleGAN, we construct a training paradigm called \textbf{RVSL} which integrates ReID and domain transformation techniques. The network is trained on semi-supervised fashion and does not require to employ the ID labels and the corresponding clear ground truths to learn hazy vehicle ReID mission in the real-world haze scenes. To further constrain the unsupervised learning process effectively, several losses are developed. Experimental results on synthetic and real-world datasets indicate that the proposed method can achieve state-of-the-art performance on hazy vehicle ReID problems. It is worth mentioning that although the proposed method is trained without real-world label information, it can achieve competitive performance compared to existing supervised methods trained on complete label information.

Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that {\em bound} the gen-error, we provide an {\em exact} expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen-error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy-to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.

It is now well understood that machine learning models, trained on data without due care, often exhibit unfair and discriminatory behavior against certain populations. Traditional algorithmic fairness research has mainly focused on supervised learning tasks, particularly classification. While fairness in unsupervised learning has received some attention, the literature has primarily addressed fair representation learning of continuous embeddings. In this paper, we conversely focus on unsupervised learning using probabilistic graphical models with discrete latent variables. We develop a fair stochastic variational inference technique for the discrete latent variables, which is accomplished by including a fairness penalty on the variational distribution that aims to respect the principles of intersectionality, a critical lens on fairness from the legal, social science, and humanities literature, and then optimizing the variational parameters under this penalty. We first show the utility of our method in improving equity and fairness for clustering using na\"ive Bayes and Gaussian mixture models on benchmark datasets. To demonstrate the generality of our approach and its potential for real-world impact, we then develop a special-purpose graphical model for criminal justice risk assessments, and use our fairness approach to prevent the inferences from encoding unfair societal biases.

Machine learning is already an important part of how modern organisation and services function. Whether in social media platforms, healthcare, or finance, machine learning models are deployed in a variety of settings. But the steps needed to train and deploy a model will differ depending on the task at hand and the data that's available. Supervised and unsupervised learning are examples of two different types of machine learning model approach. They differ in the way the models are trained and the condition of the training data that's required.

Generative Adversarial Networks (GANs) are one of the hottest topics in computer science in recent times. They are a clever way of training a generative model (unsupervised learning) by framing the problem as a supervised learning problem. The main idea is that two different models are trained simultaneously by an adversarial process. Generative adversarial networks are based on a game theoretic scenario in which the generator network must compete against an adversary. The generator network directly produces samples.

Clustering is an unsupervised machine learning technique used for discovering interesting patterns in data. An example would be grouping similar customers based on their behavior, building a spam filter, identifying fraudulent or criminal activity. In Clustering, similar items (or data points) are grouped together. However, we do not only want to group similar items together, we would also like to measure how similar or different they are. To solve this, we can easily create a scoring algorithm.