Syllabuses for curriculum learning have been developed on an ad-hoc, per task basis and little is known about the relative performance of different syllabuses. We identify a number of syllabuses used in the literature. We compare the identified syllabuses based on their effect on the speed of learning and generalization ability of a LSTM network on three sequential learning tasks. We find that the choice of syllabus has limited effect on the generalization ability of a trained network. In terms of speed of learning our results demonstrate that the best syllabus is task dependent but that a recently proposed automated curriculum learning approach - Predictive Gain, performs very competitively against all identified hand-crafted syllabuses. The best performing hand-crafted syllabus which we term Look Back and Forward combines a syllabus which steps through tasks in the order of their difficulty with a uniform distribution over all tasks. Our experimental results provide an empirical basis for the choice of syllabus on a new problem that could benefit from curriculum learning. Additionally, insights derived from our results shed light on how to successfully design new syllabuses.

We consider an online learning process to forecast a sequence of outcomes for nonconvex models. A typical measure to evaluate online learning algorithms is regret but such standard definition of regret is intractable for nonconvex models even in offline settings. Hence, gradient based definition of regrets are common for both offline and online nonconvex problems. Recently, a notion of local gradient based regret was introduced. Inspired by the concept of calibration and a local gradient based regret, we introduce another definition of regret and we discuss why our definition is more interpretable for forecasting problems. We also provide bound analysis for our regret under certain assumptions.

Nowadays, many sensitive decision-making tasks rely on automated statistical and machine learning algorithms. Examples include targeted advertising, credit scores and loans, college admissions, prediction of domestic violence, and even investment strategies for venture capital groups. There has been a growing concern about errors, unfairness, and transparency of such mechanisms from governments, civil organizations and research societies [2, 33, 40]. That is, whether or not we can prevent discrimination against protected groups and attributes (e.g., race, gender, etc). Clearly, training a machine learning algorithm with the standard aim of loss function minimization (i.e., high accuracy, low prediction error, etc) may result in predictive behaviors that are unfair towards certain groups or individuals [18, 29, 42]. In many real-world applications, we are not allowed to use some sensitive features. For example, EU anti-discrimination law prohibits the use of protected attributes (directly or indirectly) for several decision-making tasks [13]. A naive approach towards fairness is to discard sensitive attributes from training data. However, if other (seemingly) nonsensitive variables are correlated with the protected ones, the learning algorithm may use them to proxy for protected features in order to achieve a lower loss.

Statistical Machine Learning (SML) refers to a body of algorithms and methods by which computers are allowed to discover important features of input data sets which are often very large in size. The very task of feature discovery from data is essentially the meaning of the keyword `learning' in SML. Theoretical justifications for the effectiveness of the SML algorithms are underpinned by sound principles from different disciplines, such as Computer Science and Statistics. The theoretical underpinnings particularly justified by statistical inference methods are together termed as statistical learning theory. This paper provides a review of SML from a Bayesian decision theoretic point of view -- where we argue that many SML techniques are closely connected to making inference by using the so called Bayesian paradigm. We discuss many important SML techniques such as supervised and unsupervised learning, deep learning, online learning and Gaussian processes especially in the context of very large data sets where these are often employed. We present a dictionary which maps the key concepts of SML from Computer Science and Statistics. We illustrate the SML techniques with three moderately large data sets where we also discuss many practical implementation issues. Thus the review is especially targeted at statisticians and computer scientists who are aspiring to understand and apply SML for moderately large to big data sets.

University of Wisconsin-Madison Abstract Neural networks have great success in many machine learning applications, but the fundamental learning theory behind them remains largely unsolved. Learning neural networks is NPhard, but in practice, simple algorithms like stochastic gradient descent(SGD) often produce good solutions. Moreover, it is observed that overparameterization-- designing networks whose number of parameters is larger than statistically needed to perfectly fit the data -- improves both optimization and generalization, appearing to contradict traditional learning theory. In this work, we extend the theoretical understanding of two and three-layer neural networks in the overparameterized regime. We prove that, using overparameterized neural networks, one can (improperly) learn some notable hypothesis classes, including two and three-layer neural networks with fewer parameters. Moreover, the learning process can be simply done by SGD or its variants in polynomial time using polynomially many samples. We also show that for a fixed sample size, the generalization error of the solution found by some SGD variant can be made almost independent of the number of parameters in the overparameterized network. Authors sorted in alphabetical order. 1 Introduction In contrast to the widely accepted empirical success, much less theory is known. Despite a recent increase of theoretical studies, many questions remain largely open, including fundamental ones about the optimization and generalization in learning neural networks.

Learning from positive and unlabeled data or PU learning is the setting where a learner only has access to positive examples and unlabeled data. The assumption is that the unlabeled data can contain both positive and negative examples. This setting has attracted increasing interest within the machine learning literature as this type of data naturally arises in applications such as medical diagnosis and knowledge base completion. This article provides a survey of the current state of the art in PU learning. It proposes seven key research questions that commonly arise in this field and provides a broad overview of how the field has tried to address them.

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O(min{d,N} log(1/eps)) examples, where d is the ambient dimension of the problem, N is the number of learners, and eps is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners' internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners' workload and the teacher's cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.

Distance metric learning (DML) aims to find an appropriate way to reveal the underlying data relationship. It is critical in many machine learning, pattern recognition and data mining algorithms, and usually require large amount of label information (such as class labels or pair/triplet constraints) to achieve satisfactory performance. However, the label information may be insufficient in real-world applications due to the high-labeling cost, and DML may fail in this case. Transfer metric learning (TML) is able to mitigate this issue for DML in the domain of interest (target domain) by leveraging knowledge/information from other related domains (source domains). Although achieved a certain level of development, TML has limited success in various aspects such as selective transfer, theoretical understanding, handling complex data, big data and extreme cases. In this survey, we present a systematic review of the TML literature. In particular, we group TML into different categories according to different settings and metric transfer strategies, such as direct metric approximation, subspace approximation, distance approximation, and distribution approximation. A summarization and insightful discussion of the various TML approaches and their applications will be presented. Finally, we indicate some challenges and provide possible future directions.

If you're interested in the exciting world of data science, but don't know where to start, Data School is here to help. Data science can be an overwhelming field. Many people will tell you that you can't become a data scientist until you master the following: statistics, linear algebra, calculus, programming, databases, distributed computing, machine learning, visualization, experimental design, clustering, deep learning, natural language processing, and more. So, what exactly is data science? This workflow doesn't necessarily require advanced mathematics, a mastery of deep learning, or many of the other skills listed above.

"It'll automatically call police if the administration wants it to. It comes in and you see it and you can click on the video," said Christopher Ciabarra. He's describing a new technology that's based on artificial intelligence. He and Lisa Falcone are the inventors of Athena. They say it's the first A.I. security cameras used to detect guns in schools.