Classification and clustering algorithms have been proved to be successful individually in different contexts. Both of them have their own advantages and limitations. For instance, although classification algorithms are more powerful than clustering methods in predicting class labels of objects, they do not perform well when there is a lack of sufficient manually labeled reliable data. On the other hand, although clustering algorithms do not produce label information for objects, they provide supplementary constraints (e.g., if two objects are clustered together, it is more likely that the same label is assigned to both of them) that one can leverage for label prediction of a set of unknown objects. Therefore, systematic utilization of both these types of algorithms together can lead to better prediction performance. In this paper, We propose a novel algorithm, called EC3 that merges classification and clustering together in order to support both binary and multi-class classification. EC3 is based on a principled combination of multiple classification and multiple clustering methods using an optimization function. We theoretically show the convexity and optimality of the problem and solve it by block coordinate descent method. We additionally propose iEC3, a variant of EC3 that handles imbalanced training data. We perform an extensive experimental analysis by comparing EC3 and iEC3 with 14 baseline methods (7 well-known standalone classifiers, 5 ensemble classifiers, and 2 existing methods that merge classification and clustering) on 13 standard benchmark datasets. We show that our methods outperform other baselines for every single dataset, achieving at most 10% higher AUC. Moreover our methods are faster (1.21 times faster than the best baseline), more resilient to noise and class imbalance than the best baseline method.

This course will explain how to use scikit-learn to do advanced machine learning. If you are aiming to work as a professional data scientist, you need to master scikit-learn! It is expected that you have some familiarity with statistics, and python programming. It's not necessary to be an expert, but you should be able to understand what is a Gaussian distribution, code loops and functions in Python, and know the basics of a maximum likelihood estimator. The course will be entirely focused on the python implementation, and the math behind it will be omitted as much as possible.

A reliable, accurate, and affordable positioning service is highly required in wireless networks. In this paper, the novel Message Passing Hybrid Localization (MPHL) algorithm is proposed to solve the problem of cooperative distributed localization using distance and direction estimates. This hybrid approach combines two sensing modalities to reduce the uncertainty in localizing the network nodes. A statistical model is formulated for the problem, and approximate minimum mean square error (MMSE) estimates of the node locations are computed. The proposed MPHL is a distributed algorithm based on belief propagation (BP) and Markov chain Monte Carlo (MCMC) sampling. It improves the identifiability of the localization problem and reduces its sensitivity to the anchor node geometry, compared to distance-only or direction-only localization techniques. For example, the unknown location of a node can be found if it has only a single neighbor; and a whole network can be localized using only a single anchor node. Numerical results are presented showing that the average localization error is significantly reduced in almost every simulation scenario, about 50% in most cases, compared to the competing algorithms.

Science, technology, engineering, and math (STEM) fields play growing roles in national and international economies by driving innovation and generating high salary jobs. Yet, the US is lagging behind other highly industrialized nations in terms of STEM education and training. Furthermore, many economic forecasts predict a rising shortage of domestic STEM-trained professions in the US for years to come. One potential solution to this deficit is to decrease the rates at which students leave STEM-related fields in higher education, as currently over half of all students intending to graduate with a STEM degree eventually attrite. However, little quantitative research at scale has looked at causes of STEM attrition, let alone the use of machine learning to examine how well this phenomenon can be predicted. In this paper, we detail our efforts to model and predict dropout from STEM fields using one of the largest known datasets used for research on students at a traditional campus setting. Our results suggest that attrition from STEM fields can be accurately predicted with data that is routinely collected at universities using only information on students' first academic year. We also propose a method to model student STEM intentions for each academic term to better understand the timing of STEM attrition events. We believe these results show great promise in using machine learning to improve STEM retention in traditional and non-traditional campus settings.

Releasing full data records is one of the most challenging problems in data privacy. On the one hand, many of the popular techniques such as data de-identification are problematic because of their dependence on the background knowledge of adversaries. On the other hand, rigorous methods such as the exponential mechanism for differential privacy are often computationally impractical to use for releasing high dimensional data or cannot preserve high utility of original data due to their extensive data perturbation. This paper presents a criterion called plausible deniability that provides a formal privacy guarantee, notably for releasing sensitive datasets: an output record can be released only if a certain amount of input records are indistinguishable, up to a privacy parameter. This notion does not depend on the background knowledge of an adversary. Also, it can efficiently be checked by privacy tests. We present mechanisms to generate synthetic datasets with similar statistical properties to the input data and the same format. We study this technique both theoretically and experimentally. A key theoretical result shows that, with proper randomization, the plausible deniability mechanism generates differentially private synthetic data. We demonstrate the efficiency of this generative technique on a large dataset; it is shown to preserve the utility of original data with respect to various statistical analysis and machine learning measures.

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

Ji\v{r}\'i Matou\v{s}ek (1963-2015) had many breakthrough contributions in mathematics and algorithm design. His milestone results are not only profound but also elegant. By going beyond the original objects --- such as Euclidean spaces or linear programs --- Jirka found the essence of the challenging mathematical/algorithmic problems as well as beautiful solutions that were natural to him, but were surprising discoveries to the field. In this short exploration article, I will first share with readers my initial encounter with Jirka and discuss one of his fundamental geometric results from the early 1990s. In the age of social and information networks, I will then turn the discussion from geometric structures to network structures, attempting to take a humble step towards the holy grail of network science, that is to understand the network essence that underlies the observed sparse-and-multifaceted network data. I will discuss a simple result which summarizes some basic algebraic properties of personalized PageRank matrices. Unlike the traditional transitive closure of binary relations, the personalized PageRank matrices take "accumulated Markovian closure" of network data. Some of these algebraic properties are known in various contexts. But I hope featuring them together in a broader context will help to illustrate the desirable properties of this Markovian completion of networks, and motivate systematic developments of a network theory for understanding vast and ubiquitous multifaceted network data.

In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution of a product of two normally distributed variables with zero means and possibly different variances. Like other sparsity-encouraging distributions such as the Student's $t$-distribution, the normal product distribution has a sharp peak at origin, which makes it a suitable prior to encourage sparse solutions. A two-stage normal product-based hierarchical model is proposed. We resort to the variational Bayesian (VB) method to perform the inference. Simulations are conducted to illustrate the effectiveness of our proposed algorithm as compared with other state-of-the-art compressed sensing algorithms.

The spectral gap $\gamma$ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix $P$ may be unknown, yet one sample of the chain up to a fixed time $n$ may be observed. We consider here the problem of estimating $\gamma$ from this data. Let $\pi$ be the stationary distribution of $P$, and $\pi_\star = \min_x \pi(x)$. We show that if $n = \tilde{O}\bigl(\frac{1}{\gamma \pi_\star}\bigr)$, then $\gamma$ can be estimated to within multiplicative constants with high probability. When $\pi$ is uniform on $d$ states, this matches (up to logarithmic correction) a lower bound of $\tilde{\Omega}\bigl(\frac{d}{\gamma}\bigr)$ steps required for precise estimation of $\gamma$. Moreover, we provide the first procedure for computing a fully data-dependent interval, from a single finite-length trajectory of the chain, that traps the mixing time $t_{\text{mix}}$ of the chain at a prescribed confidence level. The interval does not require the knowledge of any parameters of the chain. This stands in contrast to previous approaches, which either only provide point estimates, or require a reset mechanism, or additional prior knowledge. The interval is constructed around the relaxation time $t_{\text{relax}} = 1/\gamma$, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a $1/\sqrt{n}$ rate, where $n$ is the length of the sample path.

Anima Anandkumar pioneered the research of finding global optimal in non-convex problems, a big pain point in machine learning. Our protagonist for this week's Techie Tuesdays, Anima is an academician who represents the best of both worlds--industry and academia. She has contributed significantly to major AI and ML projects at Amazon. This is a treat for all machine learning enthusiasts. In my two hours of conversation with Anima Anandkumar, Principal Scientist at Amazon Web Services, I was injected with the most potent dose of technical knowledge. Not that I didn't expect it while talking to an ex-faculty of UC Irvine (soon to be an endowed professor at Caltech), known for her research on non-convex problems (in deep learning). Our Techie Tuesdays protagonist of the week, Anima has worked towards establishing a strong collaboration between academia and industry. She follows an unconventional style of teaching, the one she would have loved as a student.