In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and improper noninformative priors to be objective in the elicitation of parameter priors. Moreover, the penalty term of the rule is shown to be the sum of half of the parameter dimension and the estimated mutual information between parameter and observed data. This helps to reveal the EEF mechanism in selecting model orders and may provide new insights into the open problems of choosing an optimal penalty term for model order selection and choosing a good prior from information theoretic viewpoints. The important example of linear model order selection is given to illustrate the algorithms and arguments. Lastly, the Bayesian EEF that uses Jeffreys prior coincides with the EEF rule derived by frequentist strategies. This shows another interesting relationship between the frequentist and Bayesian philosophies for model selection.

While there's not necessarily a "correct" answer here, it's most likely you split the bugs into four clusters. That wasn't too bad, was it? You could probably do the same with twice as many bugs, right? If you had a bit of time to spare -- or a passion for entomology -- you could probably even do this same with a hundred bugs. For a machine though, grouping ten objects into however many meaningful clusters is no small task, thanks to a mind-bending branch of maths called combinatorics, which tells us that are 115,975 different possible ways you could have grouped those ten insects together. Had there been twenty bugs, there would have been over fifty trillion possible ways of clustering them. With a hundred bugs -- there'd be many times more solutions than there are particles in the known universe. In fact, there are more than four million billion googol solutions (what's a googol?).

To summarize, it's important to spend time extracting, selecting and constructing features based on your data and it's size. It will be valuable in improving the performance of your model. Some features could be selected from a given feature set based on correlation with other predictors or with the label. If you have a small set of features, a quick brute-force approach of attempting different combinations might give you the best set of predictors. If you have a huge feature set especially when compared to the total number of data points – exploring dimensionality reduction techniques or other methods to combine multiple features together might be of help. But ultimately, though some of the methods above would help pick features, it's up to you to evaluate their value in being good predictors.

We propose a neural probabilistic structured-prediction method for transition-based natural language processing, which integrates beam search and contrastive learning. The method uses a global optimization model, which can leverage arbitrary features over non-local context. Beam search is used for efficient heuristic decoding, and contrastive learning is performed for adjusting the model according to search errors. When evaluated on both chunking and dependency parsing tasks, the proposed method achieves significant accuracy improvements over the locally normalized greedy baseline on the two tasks, respectively.

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are noisy data on black-box initial conditions, and (2) we are interested in quantifying the uncertainty associated with such noisy data in our solutions to time-dependent partial differential equations. Our method circumvents the need for spatial discretization of the differential operators by proper placement of Gaussian process priors. This is an attempt to construct structured and data-efficient learning machines, which are explicitly informed by the underlying physics that possibly generated the observed data. The effectiveness of the proposed approach is demonstrated through several benchmark problems involving linear and nonlinear time-dependent operators. In all examples, we are able to recover accurate approximations of the latent solutions, and consistently propagate uncertainty, even in cases involving very long time integration.

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular heuristics exist, but corresponding theoretical results are scarce. In this paper we investigate the asymptotic value of the normalised cut for an increasing sample assumed to arise from an underlying probability distribution, and based on this result provide recommendations for improving spectral clustering methodology. A corresponding algorithm is proposed with strong empirical performance.

An important, yet largely unstudied, problem in student data analysis is to detect misconceptions from students' responses to open-response questions. Misconception detection enables instructors to deliver more targeted feedback on the misconceptions exhibited by many students in their class, thus improving the quality of instruction. In this paper, we propose a new natural language processing-based framework to detect the common misconceptions among students' textual responses to short-answer questions. We propose a probabilistic model for students' textual responses involving misconceptions and experimentally validate it on a real-world student-response dataset. Experimental results show that our proposed framework excels at classifying whether a response exhibits one or more misconceptions. More importantly, it can also automatically detect the common misconceptions exhibited across responses from multiple students to multiple questions; this property is especially important at large scale, since instructors will no longer need to manually specify all possible misconceptions that students might exhibit.

The stochastic block model (SBM) is a random graph model with planted clusters. It is widely employed as a canonical model to study clustering and community detection, and provides generally a fertile ground to study the statistical and computational tradeoffs that arise in network and data sciences. This note surveys the recent developments that establish the fundamental limits for community detection in the SBM, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery (a.k.a., detection). The main results discussed are the phase transitions for exact recovery at the Chernoff-Hellinger threshold, the phase transition for weak recovery at the Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial recovery, the learning of the SBM parameters and the gap between information-theoretic and computational thresholds. The note also covers some of the algorithms developed in the quest of achieving the limits, in particular two-round algorithms via graph-splitting, semi-definite programming, linearized belief propagation, classical and nonbacktracking spectral methods. A few open problems are also discussed.

Which topics of machine learning are most commonly addressed in research? This question was initially answered in 2007 by doing a qualitative survey among distinguished researchers. In our study, we revisit this question from a quantitative perspective. Concretely, we collect 54K abstracts of papers published between 2007 and 2016 in leading machine learning journals and conferences. We then use machine learning in order to determine the top 10 topics in machine learning. We not only include models, but provide a holistic view across optimization, data, features, etc. This quantitative approach allows reducing the bias of surveys. It reveals new and up-to-date insights into what the 10 most prolific topics in machine learning research are. This allows researchers to identify popular topics as well as new and rising topics for their research.

Automatic Music Transcription (AMT) is one of the oldest and most well-studied problems in the field of music information retrieval. Within this challenging research field, onset detection and instrument recognition take important places in transcription systems, as they respectively help to determine exact onset times of notes and to recognize the corresponding instrument sources. The aim of this study is to explore the usefulness of multiscale scattering operators for these two tasks on plucked string instrument and piano music. After resuming the theoretical background and illustrating the key features of this sound representation method, we evaluate its performances comparatively to other classical sound representations. Using both MIDI-driven datasets with real instrument samples and real musical pieces, scattering is proved to outperform other sound representations for these AMT subtasks, putting forward its richer sound representation and invariance properties.