In recent years there has been growing attention to interpretable machine learning models which can give explanatory insights on their behavior. Thanks to their interpretability, decision trees have been intensively studied for classification tasks, and due to the remarkable advances in mixed-integer programming (MIP), various approaches have been proposed to formulate the problem of training an Optimal Classification Tree (OCT) as a MIP model. We present a novel mixed-integer quadratic formulation for the OCT problem, which exploits the generalization capabilities of Support Vector Machines for binary classification. Our model, denoted as Margin Optimal Classification Tree (MARGOT), encompasses the use of maximum margin multivariate hyperplanes nested in a binary tree structure. To enhance the interpretability of our approach, we analyse two alternative versions of MARGOT, which include feature selection constraints inducing local sparsity of the hyperplanes. First, MARGOT has been tested on non-linearly separable synthetic datasets in 2-dimensional feature space to provide a graphical representation of the maximum margin approach. Finally, the proposed models have been tested on benchmark datasets from the UCI repository. The MARGOT formulation turns out to be easier to solve than other OCT approaches, and the generated tree better generalizes on new observations. The two interpretable versions are effective in selecting the most relevant features and maintaining good prediction quality.
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Algorithmic decision making has proliferated and now impacts our daily lives in both mundane and consequential ways. Machine learning practitioners make use of a myriad of algorithms for predictive models in applications as diverse as movie recommendations, medical diagnoses, and parole recommendations without delving into the reasons driving specific predictive decisions. Machine learning algorithms in such applications are often chosen for their superior performance, however popular choices such as random forest and deep neural networks fail to provide an interpretable understanding of the predictive model. In recent years, rule-based algorithms have been used to address this issue. Wang et al. (2017) presented an or-of-and (disjunctive normal form) based classification technique that allows for classification rule mining of a single class in a binary classification; this method is also shown to perform comparably to other modern algorithms. In this work, we extend this idea to provide classification rules for both classes simultaneously. That is, we provide a distinct set of rules for both positive and negative classes. In describing this approach, we also present a novel and complete taxonomy of classifications that clearly capture and quantify the inherent ambiguity in noisy binary classifications in the real world. We show that this approach leads to a more granular formulation of the likelihood model and a simulated-annealing based optimization achieves classification performance competitive with comparable techniques. We apply our method to synthetic as well as real world data sets to compare with other related methods that demonstrate the utility of our proposal.
The twin support vector machine and its extensions have made great achievements in dealing with binary classification problems. However, it suffers from difficulties in effective solution of multi-classification and fast model selection. This work devotes to the fast regularization parameter tuning algorithm for the twin multi-class support vector machine. Specifically, a novel sample data set partition strategy is first adopted, which is the basis for the model construction. Then, combining the linear equations and block matrix theory, the Lagrangian multipliers are proved to be piecewise linear w.r.t. the regularization parameters, so that the regularization parameters are continuously updated by only solving the break points. Next, Lagrangian multipliers are proved to be 1 as the regularization parameter approaches infinity, thus, a simple yet effective initialization algorithm is devised. Finally, eight kinds of events are defined to seek for the starting event for the next iteration. Extensive experimental results on nine UCI data sets show that the proposed method can achieve comparable classification performance without solving any quadratic programming problem.
Explainable machine learning provides tools to better understand predictive models and their decisions, but many such methods are limited to producing insights with respect to a single class. When generating explanations for several classes, reasoning over them to obtain a complete view may be difficult since they can present competing or contradictory evidence. To address this issue we introduce a novel paradigm of multi-class explanations. We outline the theory behind such techniques and propose a local surrogate model based on multi-output regression trees -- called LIMEtree -- which offers faithful and consistent explanations of multiple classes for individual predictions while being post-hoc, model-agnostic and data-universal. In addition to strong fidelity guarantees, our implementation supports (interactive) customisation of the explanatory insights and delivers a range of diverse explanation types, including counterfactual statements favoured in the literature. We evaluate our algorithm with a collection of quantitative experiments, a qualitative analysis based on explainability desiderata and a preliminary user study on an image classification task, comparing it to LIME. Our contributions demonstrate the benefits of multi-class explanations and wide-ranging advantages of our method across a diverse set scenarios.
Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper, we propose to view the time series classification problem from the distribution perspective. We argue that the temporal complexity attributes to the unknown latent distributions within. To this end, we propose DIVERSIFY to learn generalized representations for time series classification. DIVERSIFY takes an iterative process: it first obtains the worst-case distribution scenario via adversarial training, then matches the distributions of the obtained sub-domains. We also present some theoretical insights. We conduct experiments on gesture recognition, speech commands recognition, wearable stress and affect detection, and sensor-based human activity recognition with a total of seven datasets in different settings. Results demonstrate that DIVERSIFY significantly outperforms other baselines and effectively characterizes the latent distributions by qualitative and quantitative analysis. Code is available at: //github.com/microsoft/robustlearn.
Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word ambiguity, (2) word synonymity, and (3) dynamic contextual dependency. To address these challenges, we propose a novel GNN-based sparse structure learning model for inductive document classification. Specifically, a document-level graph is initially generated by a disjoint union of sentence-level word co-occurrence graphs. Our model collects a set of trainable edges connecting disjoint words between sentences and employs structure learning to sparsely select edges with dynamic contextual dependencies. Graphs with sparse structures can jointly exploit local and global contextual information in documents through GNNs. For inductive learning, the refined document graph is further fed into a general readout function for graph-level classification and optimization in an end-to-end manner. Extensive experiments on several real-world datasets demonstrate that the proposed model outperforms most state-of-the-art results, and reveal the necessity to learn sparse structures for each document.
Few-shot image classification aims to classify unseen classes with limited labeled samples. Recent works benefit from the meta-learning process with episodic tasks and can fast adapt to class from training to testing. Due to the limited number of samples for each task, the initial embedding network for meta learning becomes an essential component and can largely affects the performance in practice. To this end, many pre-trained methods have been proposed, and most of them are trained in supervised way with limited transfer ability for unseen classes. In this paper, we proposed to train a more generalized embedding network with self-supervised learning (SSL) which can provide slow and robust representation for downstream tasks by learning from the data itself. We evaluate our work by extensive comparisons with previous baseline methods on two few-shot classification datasets ({\em i.e.,} MiniImageNet and CUB). Based on the evaluation results, the proposed method achieves significantly better performance, i.e., improve 1-shot and 5-shot tasks by nearly \textbf{3\%} and \textbf{4\%} on MiniImageNet, by nearly \textbf{9\%} and \textbf{3\%} on CUB. Moreover, the proposed method can gain the improvement of (\textbf{15\%}, \textbf{13\%}) on MiniImageNet and (\textbf{15\%}, \textbf{8\%}) on CUB by pretraining using more unlabeled data. Our code will be available at \hyperref[//github.com/phecy/SSL-FEW-SHOT.]{//github.com/phecy/ssl-few-shot.}
Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep Neural Networks (DNNs) to perform this task. This is surprising as deep learning has seen very successful applications in the last years. DNNs have indeed revolutionized the field of computer vision especially with the advent of novel deeper architectures such as Residual and Convolutional Neural Networks. Apart from images, sequential data such as text and audio can also be processed with DNNs to reach state-of-the-art performance for document classification and speech recognition. In this article, we study the current state-of-the-art performance of deep learning algorithms for TSC by presenting an empirical study of the most recent DNN architectures for TSC. We give an overview of the most successful deep learning applications in various time series domains under a unified taxonomy of DNNs for TSC. We also provide an open source deep learning framework to the TSC community where we implemented each of the compared approaches and evaluated them on a univariate TSC benchmark (the UCR/UEA archive) and 12 multivariate time series datasets. By training 8,730 deep learning models on 97 time series datasets, we propose the most exhaustive study of DNNs for TSC to date.
Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.
In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax
In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.
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