Uncertainty sampling, a popular active learning algorithm, is used to reduce the amount of data required to learn a classifier, but it has been observed in practice to converge to different parameters depending on the initialization and sometimes to even better parameters than standard training on all the data. In this work, we give a theoretical explanation of this phenomenon, showing that uncertainty sampling on a convex loss can be interpreted as performing a preconditioned stochastic gradient step on a smoothed version of the population zero-one loss that converges to the population zero-one loss. Furthermore, uncertainty sampling moves in a descent direction and converges to stationary points of the smoothed population zero-one loss. Experiments on synthetic and real datasets support this connection.

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface nearby the intersection and result in incorrect clustering. The Isomap algorithm uses the shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper, we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighbourhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as an input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time series characteristics exhibiting in real-world data which are not addressed properly, including 1) ability to handle seasonality fluctuation and shift, and abrupt change in trend and reminder; 2) robustness on data with anomalies; 3) applicability on time series with long seasonality period. In the paper, we propose a novel and generic time series decomposition algorithm to address these challenges. Specifically, we extract the trend component robustly by solving a regression problem using the least absolute deviations loss with sparse regularization. Based on the extracted trend, we apply the the non-local seasonal filtering to extract the seasonality component. This process is repeated until accurate decomposition is obtained. Experiments on different synthetic and real-world time series datasets demonstrate that our method outperforms existing solutions.

This work incorporates topological and geometric features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are planar sets that summarize the shape details of given data. A new metric on persistence diagrams generates input features for the classification algorithm. The metric accounts for the similarity of persistence diagrams using a linear combination of matching costs and cardinality differences. Investigation of the stability properties of this metric provides theoretical justification for the use of the metric for comparisons of such diagrams. The crystal structure of materials are successfully classified based on noisy and sparse data retrieved from synthetic Atomic Probe Tomography experiments.

Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic numerical integration technique that performs promisingly when compared to traditional Markov Chain Monte Carlo methods. However, in contrast to easily-parallelised MCMC methods, Bayesian Quadrature methods have, thus far, been essentially serial in nature, selecting a single point to sample at each step of the algorithm. We deliver methods to select batches of points at each step, based upon those recently presented in the Batch Bayesian Optimisation literature. Such parallelisation significantly reduces computation time, especially when the integrand is expensive to sample.

In unsupervised outlier ensembles, the absence of ground truth makes the combination of base detectors a challenging task. Specifically, existing parallel outlier ensembles lack a reliable way of selecting competent base detectors, affecting accuracy and stability, during model combination. In this paper, we propose a framework---called Locally Selective Combination in Parallel Outlier Ensembles (LSCP)---which addresses this issue by defining a local region around a test instance using the consensus of its nearest neighbors in randomly generated feature spaces. The top-performing base detectors in this local region are selected and combined as the model's final output. Four variants of the LSCP framework are compared with six widely used combination algorithms for parallel ensembles. Experimental results demonstrate that one of these LSCP variants consistently outperforms baseline algorithms on the majority of eighteen real-world datasets.

In the last decade, traditional dictionary learning methods have been successfully applied to various pattern classification tasks. Although these methods produce sparse representations of signals which are robust against distortions and missing data, such representations quite often turn out to be unsuitable if the final objective is signal classification. In order to overcome or at least to attenuate such a weakness, several new methods which incorporate discriminative information into sparse-inducing models have emerged in recent years. In particular, methods for discriminative dictionary learning have shown to be more accurate (in terms of signal classification) than the traditional ones, which are only focused on minimizing the total representation error. In this work, we present both a novel multi-class discriminative measure and an innovative dictionary learning method. For a given dictionary, this new measure, which takes into account not only when a particular atom is used for representing signals coming from a certain class and the magnitude of its corresponding representation coefficient, but also the effect that such an atom has in the total representation error, is capable of efficiently quantifying the degree of discriminability of each one of the atoms. On the other hand, the new dictionary construction method yields dictionaries which are highly suitable for multi-class classification tasks. Our method was tested with a widely used database for handwritten digit recognition and compared with three state-of-the-art classification methods. The results show that our method significantly outperforms the other three achieving good recognition rates and additionally, reducing the computational cost of the classifier.

Hierarchical reinforcement learning deals with the problem of breaking down large tasks into meaningful sub-tasks. Autonomous discovery of these sub-tasks has remained a challenging problem. We propose a novel method of learning sub-tasks by combining paradigms of routing in computer networks and graph based skill discovery within the options framework to define meaningful sub-goals. We apply the recent advancements of learning embeddings using Riemannian optimisation in the hyperbolic space to embed the state set into the hyperbolic space and create a model of the environment. In doing so we enforce a global topology on the states and are able to exploit this topology to learn meaningful sub-tasks. We demonstrate empirically, both in discrete and continuous domains, how these embeddings can improve the learning of meaningful sub-tasks.

A decade ago, machine learning was simply a concept but today it has changed the way we interact with technology. Devices are becoming smarter, faster and better, with Machine Learning at the helm. Thus, we have designed a comprehensive list of projects in Machine Learning course that offers a hands-on experience with ML and how to build actual projects using the Machine Learning algorithms. Furthermore, this course is a follow up to our Introduction to Machine Learning course and delves further deeper into the practical applications of Machine Learning. In this blog, we will have a look at projects divided mostly into two different levels i.e.

Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and community detection, has led to increased interest on the problem leading to a number of recent advances. Much like PCA in the feature domain, node embedding is an inherently \emph{unsupervised} task; in lack of metadata used for validation, practical methods may require standardization and limiting the use of tunable hyperparameters. Finally, node embedding methods are faced with maintaining scalability in the face of large-scale real-world graphs of ever-increasing sizes. In the present work, we propose an adaptive node embedding framework that adjusts the embedding process to a given underlying graph, in a fully unsupervised manner. To achieve this, we adopt the notion of a tunable node similarity matrix that assigns weights on paths of different length. The design of the multilength similarities ensures that the resulting embeddings also inherit interpretable spectral properties. The proposed model is carefully studied, interpreted, and numerically evaluated using stochastic block models. Moreover, an algorithmic scheme is proposed for training the model parameters effieciently and in an unsupervised manner. We perform extensive node classification, link prediction, and clustering experiments on many real world graphs from various domains, and compare with state-of-the-art scalable and unsupervised node embedding alternatives. The proposed method enjoys superior performance in many cases, while also yielding interpretable information on the underlying structure of the graph.