We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic composite gradient method that employs an incremental variance-reduced estimator for both the inner vector mapping and its Jacobian. We show that this method achieves the same orders of complexity as the best known first-order methods for minimizing expected-value and finite-sum nonconvex functions, despite the additional outer composition which renders the composite gradient estimator biased. This finding enables a much broader range of applications in machine learning to benefit from the low complexity of incremental variance-reduction methods.

Regarded as one of the most basic tools to investigate statistical properties of unsupervised data, clustering aims to group a set of objects in such a way that objects in the same cluster are more similar in some sense to each other than to those in other clusters. Typical application possibilities are to be found reaching from categorization of tissues in medical imaging to grouping internet searching results. For instance, on PET scans, cluster analysis can distinguish between different types of tissue in a three-dimensional image for many different purposes (Filipovych et al., 2011) while in the process of intelligent grouping of the files and websites, clustering algorithms create a more relevant set of search results (Marco and Navigli, 2013). Because of their wide applications, more urgent requirements for clustering algorithms that not only maintain desirable prediction accuracy but also have high computational efficiency are raised.

We study the problem of {\em distribution-independent} PAC learning of halfspaces in the presence of Massart noise. Specifically, we are given a set of labeled examples $(\mathbf{x}, y)$ drawn from a distribution $\mathcal{D}$ on $\mathbb{R}^{d+1}$ such that the marginal distribution on the unlabeled points $\mathbf{x}$ is arbitrary and the labels $y$ are generated by an unknown halfspace corrupted with Massart noise at noise rate $\eta<1/2$. The goal is to find a hypothesis $h$ that minimizes the misclassification error $\mathbf{Pr}_{(\mathbf{x}, y) \sim \mathcal{D}} \left[ h(\mathbf{x}) \neq y \right]$. We give a $\mathrm{poly}\left(d, 1/\epsilon \right)$ time algorithm for this problem with misclassification error $\eta+\epsilon$. We also provide evidence that improving on the error guarantee of our algorithm might be computationally hard. Prior to our work, no efficient weak (distribution-independent) learner was known in this model, even for the class of disjunctions. The existence of such an algorithm for halfspaces (or even disjunctions) has been posed as an open question in various works, starting with Sloan (1988), Cohen (1997), and was most recently highlighted in Avrim Blum's FOCS 2003 tutorial.

Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top performance in this context, these approaches suffer from a high inference complexity, linear w.r.t the number of categories. Different models based on the notion of binary codes have been proposed to overcome this limitation, achieving in a sublinear inference complexity. But they a priori need to decide which binary code to associate to which category before learning using more or less complex heuristics. We propose a new end-to-end model which aims at simultaneously learning to associate binary codes with categories, but also learning to map inputs to binary codes. This approach called Deep Stochastic Neural Codes (DSNC) keeps the sublinear inference complexity but do not need any a priori tuning. Experimental results on different datasets show the effectiveness of the approach w.r.t baseline methods.

Stacking methods improve the prediction performance of regression models. A simple way to stack base regressions estimators is by combining them linearly, as done by \citet{breiman1996stacked}. Even though this approach is useful from an interpretative perspective, it often does not lead to high predictive power. We propose the NN-Stacking method (NNS), which generalizes Breiman's method by allowing the linear parameters to vary with input features. This improvement enables NNS to take advantage of the fact that distinct base models often perform better at different regions of the feature space. Our method uses neural networks to estimate the stacking coefficients. We show that while our approach keeps the interpretative features of Breiman's method at a local level, it leads to better predictive power, especially in datasets with large sample sizes.

Local Interpretable Model-Agnostic Explanations (LIME) is a popular technique used to increase the interpretability and explainability of black box Machine Learning (ML) algorithms. LIME typically generates an explanation for a single prediction by any ML model by learning a simpler interpretable model (e.g. linear classifier) around the prediction through generating simulated data around the instance by random perturbation, and obtaining feature importance through applying some form of feature selection. While LIME and similar local algorithms have gained popularity due to their simplicity, the random perturbation and feature selection methods result in "instability" in the generated explanations, where for the same prediction, different explanations can be generated. This is a critical issue that can prevent deployment of LIME in a Computer-Aided Diagnosis (CAD) system, where stability is of utmost importance to earn the trust of medical professionals. In this paper, we propose a deterministic version of LIME. Instead of random perturbation, we utilize agglomerative Hierarchical Clustering (HC) to group the training data together and K-Nearest Neighbour (KNN) to select the relevant cluster of the new instance that is being explained. After finding the relevant cluster, a linear model is trained over the selected cluster to generate the explanations. Experimental results on three different medical datasets show the superiority for Deterministic Local Interpretable Model-Agnostic Explanations (DLIME), where we quantitatively determine the stability of DLIME compared to LIME utilizing the Jaccard similarity among multiple generated explanations.

We identify a fundamental issue in the popular Stochastic Neighbour Embedding (SNE and t-SNE), i.e., the "learned" similarity of any two points in high-dimensional space is not defined and cannot be computed. It underlines two previously unexplored issues in the algorithm which have undermined the quality of its final visualisation output and its ability to process large datasets. The issues are: (a) the reference probability in high-dimensional space is set based on entropy which has undefined relation with local density; and (b) the use of data independent kernel which leads to the need to determine n bandwidths for a dataset of n points. This paper establishes a principle to set the reference probability via a data-dependent kernel which has a well-defined kernel characteristic that linked directly to local density. A solution based on a recent data-dependent kernel called Isolation Kernel addresses the fundamental issue as well as its two ensuing issues. As a result, it significantly improves the quality of the final visualisation output and removes one obstacle that prevents t-SNE from processing large datasets. The solution is extremely simple, i.e., simply replacing the existing data independent kernel with Isolation Kernel, leaving the rest of the t-SNE procedure unchanged.

Face recognition is a computer vision task of identifying and verifying a person based on a photograph of their face. FaceNet is a face recognition system developed in 2015 by researchers at Google that achieved then state-of-the-art results on a range of face recognition benchmark datasets. The FaceNet system can be used broadly thanks to multiple third-party open source implementations of the model and the availability of pre-trained models. The FaceNet system can be used to extract high-quality features from faces, called face embeddings, that can then be used to train a face identification system. In this tutorial, you will discover how to develop a face detection system using FaceNet and an SVM classifier to identify people from photographs. How to Develop a Face Recognition System Using FaceNet in Keras and an SVM Classifier Photo by Peter Valverde, some rights reserved. Face recognition is the general task of identifying and verifying people from photographs of their face.

Are you interested in learning more about machine learning with Python? I recently wrote 7 Steps to Mastering Basic Machine Learning with Python -- 2019 Edition, a first step in an attempt to updated a pair of posts I wrote some time back (7 Steps to Mastering Machine Learning With Python and 7 More Steps to Mastering Machine Learning With Python), a pair of posts which are getting stale at this point, having been around for a few years. It's time to add on to the "basic" post with a set of steps for learning "intermediate" level machine learning with Python. We're talking "intermediate" in a relative sense, however, so do not expect to be a research-caliber machine learning engineer after getting through this post. The learning path is aimed at those with some understanding of programming, computer science concepts, and/or machine learning in an abstract sense, who are wanting to be able to use the implementations of machine learning algorithms of the prevalent Python libraries to build their own machine learning models.

Are you interested in learning more about machine learning with Python? I recently wrote 7 Steps to Mastering Basic Machine Learning with Python -- 2019 Edition, a first step in an attempt to updated a pair of posts I wrote some time back (7 Steps to Mastering Machine Learning With Python and 7 More Steps to Mastering Machine Learning With Python), a pair of posts which are getting stale at this point, having been around for a few years. It's time to add on to the "basic" post with a set of steps for learning "intermediate" level machine learning with Python. We're talking "intermediate" in a relative sense, however, so do not expect to be a research-caliber machine learning engineer after getting through this post. The learning path is aimed at those with some understanding of programming, computer science concepts, and/or machine learning in an abstract sense, who are wanting to be able to use the implementations of machine learning algorithms of the prevalent Python libraries to build their own machine learning models.