This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, and we connect to auto-encoder. Then, PCA with singular value decomposition, dual PCA, and kernel PCA are covered. SPCA using both scoring and Hilbert-Schmidt independence criterion are explained. Kernel SPCA using both direct and dual approaches are then introduced. We cover all cases of projection and reconstruction of training and out-of-sample data. Finally, some simulations are provided on Frey and AT&T face datasets for verifying the theory in practice.

We consider the problem of training a model under the presence of label noise. Current approaches identify samples with potentially incorrect labels and reduce their influence on the learning process by either assigning lower weights to them or completely removing them from the training set. In the first case the model however still learns from noisy labels; in the latter approach, good training data can be lost. In this paper, we propose an iterative semi-supervised mechanism for robust learning which excludes noisy labels but is still able to learn from the corresponding samples. To this end, we add an unsupervised loss term that also serves as a regularizer against the remaining label noise. We evaluate our approach on common classification tasks with different noise ratios. Our robust models outperform the state-of-the-art methods by a large margin. Especially for very large noise ratios, we achieve up to 20 % absolute improvement compared to the previous best model.

There has been much discussion recently about how fairness should be measured or enforced in classification. Individual Fairness [Dwork, Hardt, Pitassi, Reingold, Zemel, 2012], which requires that similar individuals be treated similarly, is a highly appealing definition as it gives strong guarantees on treatment of individuals. Unfortunately, the need for a task-specific similarity metric has prevented its use in practice. In this work, we propose a solution to the problem of approximating a metric for Individual Fairness based on human judgments. Our model assumes that we have access to a human fairness arbiter, who can answer a limited set of queries concerning similarity of individuals for a particular task, is free of explicit biases and possesses sufficient domain knowledge to evaluate similarity. Our contributions include definitions for metric approximation relevant for Individual Fairness, constructions for approximations from a limited number of realistic queries to the arbiter on a sample of individuals, and learning procedures to construct hypotheses for metric approximations which generalize to unseen samples under certain assumptions of learnability of distance threshold functions.

The fundamental assignment problem is in search of welfare maximization mechanisms to allocate items to agents when the private preferences over indivisible items are provided by self-interested agents. The mainstream mechanism \textit{Random Priority} is asymptotically the best mechanism for this purpose, when comparing its welfare to the optimal social welfare using the canonical \textit{worst-case approximation ratio}. Despite its popularity, the efficiency loss indicated by the worst-case ratio does not have a constant bound. Recently, [Deng, Gao, Zhang 2017] show that when the agents' preferences are drawn from a uniform distribution, its \textit{average-case approximation ratio} is upper bounded by 3.718. They left it as an open question of whether a constant ratio holds for general scenarios. In this paper, we offer an affirmative answer to this question by showing that the ratio is bounded by $1/\mu$ when the preference values are independent and identically distributed random variables, where $\mu$ is the expectation of the value distribution. This upper bound also improves the upper bound of 3.718 in [Deng, Gao, Zhang 2017] for the Uniform distribution. Moreover, under mild conditions, the ratio has a \textit{constant} bound for any independent random values. En route to these results, we develop powerful tools to show the insights that in most instances the efficiency loss is small.

Cognitive diagnosis is a fundamental and crucial task in many educational applications, e.g., computer adaptive test and cognitive assignments. Item Response Theory (IRT) is a classical cognitive diagnosis method which can provide interpretable parameters (i.e., student latent trait, question discrimination, and difficulty) for analyzing student performance. However, traditional IRT ignores the rich information in question texts, cannot diagnose knowledge concept proficiency, and it is inaccurate to diagnose the parameters for the questions which only appear several times. To this end, in this paper, we propose a general Deep Item Response Theory (DIRT) framework to enhance traditional IRT for cognitive diagnosis by exploiting semantic representation from question texts with deep learning. In DIRT, we first use a proficiency vector to represent students' proficiency in knowledge concepts and embed question texts and knowledge concepts to dense vectors by Word2Vec. Then, we design a deep diagnosis module to diagnose parameters in traditional IRT by deep learning techniques. Finally, with the diagnosed parameters, we input them into the logistic-like formula of IRT to predict student performance. Extensive experimental results on real-world data clearly demonstrate the effectiveness and interpretation power of DIRT framework.

Artificial intelligence (AI) has the potential to help tackle some of the world's most challenging social problems. To analyze potential applications for social good, we compiled a library of about 160 AI social-impact use cases. They suggest that existing capabilities could contribute to tackling cases across all 17 of the UN's sustainable-development goals, potentially helping hundreds of millions of people in both advanced and emerging countries. Real-life examples of AI are already being applied in about one-third of these use cases, albeit in relatively small tests. They range from diagnosing cancer to helping blind people navigate their surroundings, identifying victims of online sexual exploitation, and aiding disaster-relief efforts (such as the flooding that followed Hurricane Harvey in 2017). AI is only part of a much broader tool kit of measures that can be used to tackle societal issues, however. For now, issues such as data accessibility and shortages of AI talent constrain its application for social good. This article is a condensed version of our discussion paper, Notes from the AI frontier: Applying AI for social good (PDF–3MB).

Now i need to predict, how much we need to pay for purchasing Product named "Y" on new Date "D1" at Location/Place "P1" and same 5-10 other features.

A school district in western New York is launching a first-of-its-kind facial recognition system, generating new privacy concerns about the powerful but controversial technology. The Lockport city school district is beginning implementation of the Aegis facial recognition system this week, officials said, with the technology expected to be fully up and running in time for the new school year in September. "Much to our dismay, school shootings continue to occur in our country. In many cases, these shootings involve students connected to the schools where these horrific incidents occur," superintendent Michelle Bradley said in a message to parents. "The Lockport city school district continues to make school security a priority."

Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes are often only partially observed, introducing learning problems such as link prediction which must be solved prior to optimization. We propose an approach to integrate a differentiable proxy for common graph optimization problems into training of machine learning models for tasks such as link prediction. This allows the model to focus specifically on the downstream task that its predictions will be used for. Experimental results show that our end-to-end system obtains better performance on example optimization tasks than can be obtained by combining state of the art link prediction methods with expert-designed graph optimization algorithms.

Recent advances in deep learning have facilitated the demand of neural models for real applications. In practice, these applications often need to be deployed with limited resources while keeping high accuracy. This paper touches the core of neural models in NLP, word embeddings, and presents a new embedding distillation framework that remarkably reduces the dimension of word embeddings without compromising accuracy. A novel distillation ensemble approach is also proposed that trains a high-efficient student model using multiple teacher models. In our approach, the teacher models play roles only during training such that the student model operates on its own without getting supports from the teacher models during decoding, which makes it eighty times faster and lighter than other typical ensemble methods. All models are evaluated on seven document classification datasets and show a significant advantage over the teacher models for most cases. Our analysis depicts insightful transformation of word embeddings from distillation and suggests a future direction to ensemble approaches using neural models.