It's almost admission season and I've couple of friends who are in panic mode waiting for a call from the universities they've applied at. This made me think -- How can we predict whether a student will get an admit or not? What are the parameters for selection? Can it be mathematically expressed? All of these questions started popping up, so I decided to work out this problem and help my friend calm his nerves.

Epanechnikov Mean Shift is a simple yet empirically very effective algorithm for clustering. It localizes the centroids of data clusters via estimating modes of the probability distribution that generates the data points, using the "optimal" Epanechnikov kernel density estimator. However, since the procedure involves non-smooth kernel density functions,the convergence behavior of Epanechnikov mean shift lacks theoretical support as of this writing---most of the existing analyses are based on smooth functions and thus cannot be applied to Epanechnikov Mean Shift. In this work, we first show that the original Epanechnikov Mean Shift may indeed terminate at a non-critical point, due to the non-smoothness nature. Based on our analysis, we propose a simple remedy to fix it. The modified Epanechnikov Mean Shift is guaranteed to terminate at a local maximum of the estimated density, which corresponds to a cluster centroid, within a inite number of iterations. We also propose a way to avoid running the Mean Shift iterates from every data point, while maintaining good clustering accuracies under non-overlapping spherical Gaussian mixture models. This further pushes Epanechnikov Mean Shift to handle very large and high-dimensional data sets. Experiments show surprisingly good performance compared to the Lloyd's K-means algorithm and the EM algorithm.

Feature engineering is a crucial step in the process of predictive modeling. It involves the transformation of given feature space, typically using mathematical functions, with the objective of reducing the modeling error for a given target. However, there is no well-defined basis for performing effective feature engineering. It involves domain knowledge, intuition, and most of all, a lengthy process of trial and error. The human attention involved in overseeing this process significantly influences the cost of model generation. We present a new framework to automate feature engineering. It is based on performance driven exploration of a transformation graph, which systematically and compactly captures the space of given options. A highly efficient exploration strategy is derived through reinforcement learning on past examples.

Credit card transactions predicted to be fraudulent by automated detection systems are typically handed over to human experts for verification. To limit costs, it is standard practice to select only the most suspicious transactions for investigation. We claim that a trade-off between exploration and exploitation is imperative to enable adaptation to changes in behavior (concept drift). Exploration consists of the selection and investigation of transactions with the purpose of improving predictive models, and exploitation consists of investigating transactions detected to be suspicious. Modeling the detection of fraudulent transactions as rewarding, we use an incremental Regression Tree learner to create clusters of transactions with similar expected rewards. This enables the use of a Contextual Multi-Armed Bandit (CMAB) algorithm to provide the exploration/exploitation trade-off. We introduce a novel variant of a CMAB algorithm that makes use of the structure of this tree, and use Semi-Supervised Learning to grow the tree using unlabeled data. The approach is evaluated on a real dataset and data generated by a simulator that adds concept drift by adapting the behavior of fraudsters to avoid detection. It outperforms frequently used offline models in terms of cumulative rewards, in particular in the presence of concept drift.

Support Vector Machines (SVMs) are excellent candidate solutions to solving multi-class problems, and multi-class SVMs can be trained by several different methods. Different training methods commonly produce SVMs with different effectiveness, and no multi-class SVM training method always outperforms other multi-class SVM training methods on all problems. This raises difficulty for practitioners to choose the best training method for a given problem. In this work, we propose a Multi-class Method Selection (MMS) approach to help users select the most appropriate method among one-versus-one (OVO), one-versus-all (OVA) and structural SVMs (SSVMs) for a given problem. Our key idea is to select the training method based on the distribution of training data and the similarity between different classes. Using the distribution and class similarity, we estimate the unclassifiable rate of each multi-class SVM training method, and select the training method with the minimum unclassifiable rate. Our initial findings show: (i) SSVMs with linear kernel perform worse than OVO and OVA; (ii) MMS often produces SVM classifiers that can confidently classify unseen instances.

In this case, we would be interested used in biological and social sciences to predict events and to in identifying a segment of the population for which describe possible relationships between variables. When addressing a linear rule is highly predictive of the price of certain cars, the task of prediction, machine learning and statistics whereas this linear rule may not provide a good prediction commonly focus on capturing the vast majority of data, overall in the larger population. Let us imagine that for this occasionally ignoring a segment of the population as "outliers" data set, and for a target fraction of the population, we found or "noise," which could be helpful to better understand a simple rule that describes the subpopulation, along with the data. Previous work by Juba (2016) gave an algorithm its linear fit.

Recurrent neural language models are the state-of-the-art models for language modeling. When the vocabulary size is large, the space taken to store the model parameters becomes the bottleneck for the use of recurrent neural language models. In this paper, we introduce a simple space compression method that randomly shares the structured parameters at both the input and output embedding layers of the recurrent neural language models to significantly reduce the size of model parameters, but still compactly represent the original input and output embedding layers. The method is easy to implement and tune. Experiments on several data sets showthat the new method can get similar perplexity and BLEU score results whileonly using a very tiny fraction of parameters.

It is challenging to perform k-means clustering on a large scale dataset efficiently. One of the reasons is that k-means needs to scan a batch of training data to update the cluster centers at every iteration, which is time-consuming. In the paper, we propose a variance reduced k-mean VRKM, which outperforms the state-of-the-art method, and obtain 4× speedup for large-scale clustering. The source code is available on https://github.com/YaweiZhao/VRKM_sofia-ml.

Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowadays. However, in spite of hundreds of papers on the topic being published every year, current theoretical understanding and practical implementations of such tasks, in particular of clustering, is very rudimentary. This note focuses on clustering. The first challenge I address is model selection---how should a user pick an appropriate clustering tool for a given clustering problem, and how should the parameters of such an algorithmic tool be tuned? In contrast with other common computational tasks, for clustering, different algorithms often yield drastically different outcomes. Therefore, the choice of a clustering algorithm may play a crucial role in the usefulness of an output clustering solution. However, currently there exists no methodical guidance for clustering tool selection for a given clustering task. I argue the severity of this problem and describe some recent proposals aiming to address this crucial lacuna.

We propose a simple approach to visual alignment, focusing on the illustrative task of facial landmark estimation. While most prior work treats this as a regression problem, we instead formulate it as a discrete K-way classification task, where a classifier is trained to return one of K discrete alignments. One crucial benefit of a classifier is the ability to report back a (softmax) distribution over putative alignments. We demonstrate that this distribution is a rich representation that can be marginalized (to generate uncertainty estimates over groups of landmarks) and conditioned on (to incorporate top-down context, provided by temporal constraints in a video stream or an interactive human user). Such capabilities are difficult to integrate into classic regression-based approaches. We study performance as a function of the number of classes K, including the extreme "exemplar class" setting where K is equal to the number of training examples (140K in our setting). Perhaps surprisingly, we show that classifiers can still be learned in this setting. When compared to prior work in classification, our K is unprecedentedly large, including many "fine-grained" classes that are very similar. We address these issues by using a multi-label loss function that allows for training examples to be non-uniformly shared across discrete classes. We perform a comprehensive experimental analysis of our method on standard benchmarks, demonstrating state-of-the-art results for facial alignment in videos.