This work explores adaptations of successful multi-armed bandits policies to the online contextual bandits scenario with binary rewards using binary classification algorithms such as logistic regression as black-box oracles. Some of these adaptations are achieved through bootstrapping or approximate bootstrapping, while others rely on other forms of randomness, resulting in more scalable approaches than previous works, and the ability to work with any type of classification algorithm. In particular, the Adaptive-Greedy algorithm shows a lot of promise, in many cases achieving better performance than upper confidence bound and Thompson sampling strategies, at the expense of more hyperparameters to tune.
Extracting actionable insight from Electronic Health Records (EHRs) poses several challenges for traditional machine learning approaches. Patients are often missing data relative to each other; the data comes in a variety of modalities, such as multivariate time series, free text, and categorical demographic information; important relationships among patients can be difficult to detect; and many others. In this work, we propose a novel approach to address these first three challenges using a representation learning scheme based on message passing. We show that our proposed approach is competitive with or outperforms the state of the art for predicting in-hospital mortality (binary classification), the length of hospital visits (regression) and the discharge destination (multiclass classification).
Classification, the process of assigning a label (or class) to an observation given its features, is a common task in many applications. Nonetheless in most real-life applications, the labels can not be fully explained by the observed features. Indeed there can be many factors hidden to the modellers. The unexplained variation is then treated as some random noise which is handled differently depending on the method retained by the practitioner. This work focuses on two simple and widely used supervised classification algorithms: discrete choice models and artificial neural networks in the context of binary classification. Through various numerical experiments involving continuous or discrete explanatory features, we present a comparison of the retained methods' performance in presence of missing variables. The impact of the distribution of the two classes in the training data is also investigated. The outcomes of those experiments highlight the fact that artificial neural networks outperforms the discrete choice models, except when the distribution of the classes in the training data is highly unbalanced. Finally, this work provides some guidelines for choosing the right classifier with respect to the training data.
In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem and can be solved using a gradient descent algorithm. We also provide qualitative analysis on fitness to data of this function fitting method. The function fitting problem is also shown to be a solution of a linear, weak partial differential equation(PDE). We describe a way to fit a Sobolev function by giving a method to choose the optimal $\lambda$ parameter. We describe a closed-form solution to the derived PDE, which enables the parametrization of the solution function. We describe a simple numerical solution using a gradient descent algorithm, that converges uniformly to the actual solution. As the functional of the minimization problem is a quadratic form, there also exists a numerical method using linear algebra. Lastly, we give some numerical examples and also numerically demonstrate its application to a binary classification problem.
Epilepsy is the most common neurological disorder and an accurate forecast of seizures would help to overcome the patient's uncertainty and helplessness. In this contribution, we present and discuss a novel methodology for the classification of intracranial electroencephalography (iEEG) for seizure prediction. Contrary to previous approaches, we categorically refrain from an extraction of hand-crafted features and use a convolutional neural network (CNN) topology instead for both the determination of suitable signal characteristics and the binary classification of preictal and interictal segments. Three different models have been evaluated on public datasets with long-term recordings from four dogs and three patients. Overall, our findings demonstrate the general applicability. In this work we discuss the strengths and limitations of our methodology.
The identification and quantification of markers in medical images is critical for diagnosis, prognosis, and disease management. Supervised machine learning enables the detection and exploitation of findings that are known a priori after annotation of training examples by experts. However, supervision does not scale well, due to the amount of necessary training examples, and the limitation of the marker vocabulary to known entities. In this proof-of-concept study, we propose unsupervised identification of anomalies as candidates for markers in retinal Optical Coherence Tomography (OCT) imaging data without a constraint to a priori definitions. We identify and categorize marker candidates occurring frequently in the data, and demonstrate that these markers show predictive value in the task of detecting disease. A careful qualitative analysis of the identified data driven markers reveals how their quantifiable occurrence aligns with our current understanding of disease course, in early- and late age-related macular degeneration (AMD) patients. A multi-scale deep denoising autoencoder is trained on healthy images, and a one-class support vector machine identifies anomalies in new data. Clustering in the anomalies identifies stable categories. Using these markers to classify healthy-, early AMD- and late AMD cases yields an accuracy of 81.40%. In a second binary classification experiment on a publicly available data set (healthy vs. intermediate AMD) the model achieves an area under the ROC curve of 0.944.
Decoding EEG signals of different mental states is a challenging task for brain-computer interfaces (BCIs) due to nonstationarity of perceptual decision processes. This paper presents a novel boosted convolutional neural networks (ConvNets) decoding scheme for motor imagery (MI) EEG signals assisted by the multiwavelet-based time-frequency (TF) causality analysis. Specifically, multiwavelet basis functions are first combined with Geweke spectral measure to obtain high-resolution TF-conditional Granger causality (CGC) representations, where a regularized orthogonal forward regression (ROFR) algorithm is adopted to detect a parsimonious model with good generalization performance. The causality images for network input preserving time, frequency and location information of connectivity are then designed based on the TF-CGC distributions of alpha band multichannel EEG signals. Further constructed boosted ConvNets by using spatio-temporal convolutions as well as advances in deep learning including cropping and boosting methods, to extract discriminative causality features and classify MI tasks. Our proposed approach outperforms the competition winner algorithm with 12.15% increase in average accuracy and 74.02% decrease in associated inter subject standard deviation for the same binary classification on BCI competition-IV dataset-IIa. Experiment results indicate that the boosted ConvNets with causality images works well in decoding MI-EEG signals and provides a promising framework for developing MI-BCI systems.
Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists when the data is non-separable, but fails to exist when the data is separable. First-order methods are the algorithms of choice for solving large-scale instances of the logistic regression problem. In this paper, we introduce a pair of condition numbers that measure the degree of non-separability or separability of a given dataset in the setting of binary classification, and we study how these condition numbers relate to and inform the properties and the convergence guarantees of first-order methods. When the training data is non-separable, we show that the degree of non-separability naturally enters the analysis and informs the properties and convergence guarantees of two standard first-order methods: steepest descent (for any given norm) and stochastic gradient descent. Expanding on the work of Bach, we also show how the degree of non-separability enters into the analysis of linear convergence of steepest descent (without needing strong convexity), as well as the adaptive convergence of stochastic gradient descent. When the training data is separable, first-order methods rather curiously have good empirical success, which is not well understood in theory. In the case of separable data, we demonstrate how the degree of separability enters into the analysis of $\ell_2$ steepest descent and stochastic gradient descent for delivering approximate-maximum-margin solutions with associated computational guarantees as well. This suggests that first-order methods can lead to statistically meaningful solutions in the separable case, even though the ML solution does not exist.
Generalized additive models (GAMs) are favored in many regression and binary classification problems because they are able to fit complex, nonlinear functions while still remaining interpretable. In the first part of this paper, we generalize a state-of-the-art GAM learning algorithm based on boosted trees to the multiclass setting, and show that this multiclass algorithm outperforms existing GAM learning algorithms and sometimes matches the performance of full complexity models such as gradient boosted trees. In the second part, we turn our attention to the interpretability of GAMs in the multiclass setting. Surprisingly, the natural interpretability of GAMs breaks down when there are more than two classes. Naive interpretation of multiclass GAMs can lead to false conclusions. Inspired by binary GAMs, we identify two axioms that any additive model must satisfy in order to not be visually misleading. We then develop a technique called Additive Post-Processing for Interpretability (API), that provably transforms a pre-trained additive model to satisfy the interpretability axioms without sacrificing accuracy. The technique works not just on models trained with our learning algorithm, but on any multiclass additive model, including multiclass linear and logistic regression. We demonstrate the effectiveness of API on a 12-class infant mortality dataset.
Recent studies on disparate impact in machine learning applications have sparked a debate around the concept of fairness along with attempts to formalize its different criteria. Many of these approaches focus on reducing prediction errors while maximizing sole utility of the institution. This work seeks to reconceptualize and critically frame the existing discourse on fairness by underlining the implicit biases embedded in common understandings of fairness in the literature and how they contrast with its corresponding economic and legal definitions. This paper expands the concept of utility and fairness by bringing in concepts from established literature in welfare economics and game theory. We then translate these concepts for the algorithmic prediction domain by defining a formalization of Nash Welfare Product that seeks to expand utility by collapsing that of the institution using the prediction tool and the individual subject to the prediction into one function. We then apply a modulating function that makes the fairness and welfare trade-offs explicit based on designated policy goals and then apply it to a temporal model to take into account the effects of decisions beyond the scope of one-shot predictions. We apply this on a binary classification problem and present results of a multi-epoch simulation based on the UCI Adult Income dataset and a test case analysis of the ProPublica recidivism dataset that show that expanding the concept of utility results in a fairer distribution correcting for the embedded biases in the dataset without sacrificing the classifier accuracy.
Cloud detection plays a very important role in the process of remote sensing images. This paper designs a super-pixel level cloud detection method based on convolutional neural network (CNN) and deep forest. Firstly, remote sensing images are segmented into super-pixels through the combination of SLIC and SEEDS. Structured forests is carried out to compute edge probability of each pixel, based on which super-pixels are segmented more precisely. Segmented super-pixels compose a super-pixel level remote sensing database. Though cloud detection is essentially a binary classification problem, our database is labeled into four categories: thick cloud, cirrus cloud, building and other culture, to improve the generalization ability of our proposed models. Secondly, super-pixel level database is used to train our cloud detection models based on CNN and deep forest. Considering super-pixel level remote sensing images contain less semantic information compared with general object classification database, we propose a Hierarchical Fusion CNN (HFCNN). It takes full advantage of low-level features like color and texture information and is more applicable to cloud detection task. In test phase, every super-pixel in remote sensing images is classified by our proposed models and then combined to recover final binary mask by our proposed distance metric, which is used to determine ambiguous super-pixels. Experimental results show that, compared with conventional methods, HFCNN can achieve better precision and recall.
Feature Selection (FS) plays an important role in learning and classification tasks. The object of FS is to select the relevant and non-redundant features. Considering the huge amount number of features in real-world applications, FS methods using batch learning technique can't resolve big data problem especially when data arrive sequentially. In this paper, we propose an online feature selection system which resolves this problem. More specifically, we treat the problem of online supervised feature selection for binary classification as a decision-making problem. A philosophical vision to this problem leads to a hybridization between two important domains: feature selection using online learning technique (OFS) and automated negotiation (AN). The proposed OFS system called MOANOFS (Multi-Objective Automated Negotiation based Online Feature Selection) uses two levels of decision. In the first level, from n learners (or OFS methods), we decide which are the k trustful ones (with high confidence or trust value). These elected k learners will participate in the second level. In this level, we integrate our proposed Multilateral Automated Negotiation based OFS (MANOFS) method to decide finally which is the best solution or which are relevant features. We show that MOANOFS system is applicable to different domains successfully and achieves high accuracy with several real-world applications. Index Terms: Feature selection, online learning, multi-objective automated negotiation, trust, classification, big data.
Text analytics based on supervised machine learning classifiers has shown great promise in a multitude of domains, but has yet to be applied to Seismology. We test various standard models (Naive Bayes, k-Nearest Neighbors, Support Vector Machines, and Random Forests) on a seismological corpus of 100 articles related to the topic of precursory accelerating seismicity, spanning from 1988 to 2010. This corpus was labelled in Mignan (2011) with the precursor whether explained by critical processes (i.e., cascade triggering) or by other processes (such as signature of main fault loading). We investigate rather the classification process can be automatized to help analyze larger corpora in order to better understand trends in earthquake predictability research. We find that the Naive Bayes model performs best, in agreement with the machine learning literature for the case of small datasets, with cross-validation accuracies of 86% for binary classification. For a refined multiclass classification ('non-critical process' < 'agnostic' < 'critical process assumed' < 'critical process demonstrated'), we obtain up to 78% accuracy. Prediction on a dozen of articles published since 2011 shows however a weak generalization with a F1-score of 60%, only slightly better than a random classifier, which can be explained by a change of authorship and use of different terminologies. Yet, the model shows F1-scores greater than 80% for the two multiclass extremes ('non-critical process' versus 'critical process demonstrated') while it falls to random classifier results (around 25%) for papers labelled 'agnostic' or 'critical process assumed'. Those results are encouraging in view of the small size of the corpus and of the high degree of abstraction of the labelling. Domain knowledge engineering remains essential but can be made transparent by an investigation of Naive Bayes keyword posterior probabilities.
(Mini-batch) Stochastic Gradient Descent is a popular optimization method which has been applied to many machine learning applications. But a rather high variance introduced by the stochastic gradient in each step may slow down the convergence. In this paper, we propose the antithetic sampling strategy to reduce the variance by taking advantage of the internal structure in dataset. Under this new strategy, stochastic gradients in a mini-batch are no longer independent but negatively correlated as much as possible, while the mini-batch stochastic gradient is still an unbiased estimator of full gradient. For the binary classification problems, we just need to calculate the antithetic samples in advance, and reuse the result in each iteration, which is practical. Experiments are provided to confirm the effectiveness of the proposed method.
We consider a model of robust learning in an adversarial environment. The learner gets uncorrupted training data with access to possible corruptions that may be affected by the adversary during testing. The learner's goal is to build a robust classifier, which will be tested on future adversarial examples. The adversary is limited to $k$ possible corruptions for each input. We model the learner-adversary interaction as a zero-sum game. This model is closely related to the adversarial examples model of Schmidt et al. (2018); Madry et al. (2017). Our main results consist of generalization bounds for the binary and multiclass classification, as well as the real-valued case (regression). For the binary classification setting, we both tighten the generalization bound of Feige et al. (2015), and are also able to handle infinite hypothesis classes. The sample complexity is improved from $O(\frac{1}{\epsilon^4}\log(\frac{|H|}{\delta}))$ to $O\big(\frac{1}{\epsilon^2}(kVC(H)\log^{\frac{3}{2}+\alpha}(kVC(H))+\log(\frac{1}{\delta})\big)$ for any $\alpha > 0$. Additionally, we extend the algorithm and generalization bound from the binary to the multiclass and real-valued cases. Along the way, we obtain results on fat-shattering dimension and Rademacher complexity of $k$-fold maxima over function classes; these may be of independent interest. For binary classification, the algorithm of Feige et al. (2015) uses a regret minimization algorithm and an ERM oracle as a black box; we adapt it for the multiclass and regression settings. The algorithm provides us with near-optimal policies for the players on a given training sample.
In the problem of domain adaptation for binary classification, the learner is presented with labeled examples from a source domain, and must correctly classify unlabeled examples from a target domain, which may differ from the source. Previous work on this problem has assumed that the performance measure of interest is the expected value of some loss function. We introduce a new Neyman-Pearson-like criterion and argue that, for this optimality criterion, stronger domain adaptation results are possible than what has previously been established. In particular, we study a class of domain adaptation problems that generalizes both the covariate shift assumption and a model for feature-dependent label noise, and establish optimal classification on the target domain despite not having access to labelled data from this domain.
Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze-Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman-Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is derived from a multicolored Euclidean minimal spanning tree (MST) that spans the merged samples. We obtain a concentration inequality for the Friedman-Rafsky estimator of the Henze-Penrose divergence. We validate our results experimentally and illustrate their application to real datasets.
In binary classification, there are situations where negative (N) data are too diverse to be fully labeled and we often resort to positive-unlabeled (PU) learning in these scenarios. However, collecting a non-representative N set that contains only a small portion of all possible N data can often be much easier in practice. This paper studies a novel classification framework which incorporates such biased N (bN) data in PU learning. We provide a method based on empirical risk minimization to address this PUbN classification problem. Our approach can be regarded as a novel example-weighting algorithm, with the weight of each example computed through a preliminary step that draws inspiration from PU learning. We also derive an estimation error bound for the proposed method. Experimental results demonstrate the effectiveness of our algorithm in not only PUbN learning scenarios but also ordinary PU learning scenarios on several benchmark datasets.
The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, while the overlap is an ambiguity region which could belong to either class. Instead of plug-in approaches, we propose a support vector classifier to construct confidence sets in a flexible manner. Theoretically, we show that the proposed learner can control the non-coverage rates and minimize the ambiguity with high probability. Efficient algorithms are developed and numerical studies illustrate the effectiveness of the proposed method.
Outlier detection is an important topic in machine learning and has been used in a wide range of applications. In this paper, we approach outlier detection as a binary-classification issue by sampling potential outliers from a uniform reference distribution. However, due to the sparsity of data in high-dimensional space, a limited number of potential outliers may fail to provide sufficient information to assist the classifier in describing a boundary that can separate outliers from normal data effectively. To address this, we propose a novel Single-Objective Generative Adversarial Active Learning (SO-GAAL) method for outlier detection, which can directly generate informative potential outliers based on the mini-max game between a generator and a discriminator. Moreover, to prevent the generator from falling into the mode collapsing problem, the stop node of training should be determined when SO-GAAL is able to provide sufficient information. But without any prior information, it is extremely difficult for SO-GAAL. Therefore, we expand the network structure of SO-GAAL from a single generator to multiple generators with different objectives (MO-GAAL), which can generate a reasonable reference distribution for the whole dataset. We empirically compare the proposed approach with several state-of-the-art outlier detection methods on both synthetic and real-world datasets. The results show that MO-GAAL outperforms its competitors in the majority of cases, especially for datasets with various cluster types or high irrelevant variable ratio.