The ability to control for the kinds of information encoded in neural representation has a variety of use cases, especially in light of the challenge of interpreting these models. We present Iterative Null-space Projection (INLP), a novel method for removing information from neural representations. Our method is based on repeated training of linear classifiers that predict a certain property we aim to remove, followed by projection of the representations on their null-space. By doing so, the classifiers become oblivious to that target property, making it hard to linearly separate the data according to it. While applicable for multiple uses, we evaluate our method on bias and fairness use-cases, and show that our method is able to mitigate bias in word embeddings, as well as to increase fairness in a setting of multi-class classification.
Deep convolutional neural networks (CNNs) trained with logistic and softmax losses have made significant advancement in visual recognition tasks in computer vision. When training data exhibit class imbalances, the class-wise reweighted version of logistic and softmax losses are often used to boost performance of the unweighted version. In this paper, motivated to explain the reweighting mechanism, we explicate the learning property of those two loss functions by analyzing the necessary condition (e.g., gradient equals to zero) after training CNNs to converge to a local minimum. The analysis immediately provides us explanations for understanding (1) quantitative effects of the class-wise reweighting mechanism: deterministic effectiveness for binary classification using logistic loss yet indeterministic for multi-class classification using softmax loss; (2) disadvantage of logistic loss for single-label multi-class classification via one-vs.-all approach, which is due to the averaging effect on predicted probabilities for the negative class (e.g., non-target classes) in the learning process. With the disadvantage and advantage of logistic loss disentangled, we thereafter propose a novel reweighted logistic loss for multi-class classification. Our simple yet effective formulation improves ordinary logistic loss by focusing on learning hard non-target classes (target vs. non-target class in one-vs.-all) and turned out to be competitive with softmax loss. We evaluate our method on several benchmark datasets to demonstrate its effectiveness.
In this paper, we study the formalism of unsupervised multi-class domain adaptation (multi-class UDA), which underlies a few recent algorithms whose learning objectives are only motivated empirically. Multi-Class Scoring Disagreement (MCSD) divergence is presented by aggregating the absolute margin violations in multi-class classification, and this proposed MCSD is able to fully characterize the relations between any pair of multi-class scoring hypotheses. By using MCSD as a measure of domain distance, we develop a new domain adaptation bound for multi-class UDA; its data-dependent, probably approximately correct bound is also developed that naturally suggests adversarial learning objectives to align conditional feature distributions across source and target domains. Consequently, an algorithmic framework of Multi-class Domain-adversarial learning Networks (McDalNets) is developed, and its different instantiations via surrogate learning objectives either coincide with or resemble a few recently popular methods, thus (partially) underscoring their practical effectiveness. Based on our identical theory for multi-class UDA, we also introduce a new algorithm of Domain-Symmetric Networks (SymmNets), which is featured by a novel adversarial strategy of domain confusion and discrimination. SymmNets affords simple extensions that work equally well under the problem settings of either closed set, partial, or open set UDA. We conduct careful empirical studies to compare different algorithms of McDalNets and our newly introduced SymmNets. Experiments verify our theoretical analysis and show the efficacy of our proposed SymmNets. In addition, we have made our implementation code publicly available.
It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly accurate. If this input noise is not taken into account, a supervised machine learning method is expected to perform sub-optimally. In this paper, we focus on multi-class classification problems and use Gaussian processes (GPs) as the underlying classifier. Motivated by a data set coming from the astrophysics domain, we hypothesize that the observed data may contain noise in the inputs. Therefore, we devise several multi-class GP classifiers that can account for input noise. Such classifiers can be efficiently trained using variational inference to approximate the posterior distribution of the latent variables of the model. Moreover, in some situations, the amount of noise can be known before-hand. If this is the case, it can be readily introduced in the proposed methods. This prior information is expected to lead to better performance results. We have evaluated the proposed methods by carrying out several experiments, involving synthetic and real data. These include several data sets from the UCI repository, the MNIST data set and a data set coming from astrophysics. The results obtained show that, although the classification error is similar across methods, the predictive distribution of the proposed methods is better, in terms of the test log-likelihood, than the predictive distribution of a classifier based on GPs that ignores input noise.
The development of deep convolutional neural network architecture is critical to the improvement of image classification task performance. Many image classification studies use deep convolutional neural network and focus on modifying the network structure to improve image classification performance. Conversely, our study focuses on loss function design. Cross-entropy Loss (CEL) has been widely used for training deep convolutional neural network for the task of multi-class classification. Although CEL has been successfully implemented in several image classification tasks, it only focuses on the posterior probability of the correct class. For this reason, a negative log likelihood ratio loss (NLLR) was proposed to better differentiate between the correct class and the competing incorrect ones. However, during the training of the deep convolutional neural network, the value of NLLR is not always positive or negative, which severely affects the convergence of NLLR. Our proposed competing ratio loss (CRL) calculates the posterior probability ratio between the correct class and the competing incorrect classes to further enlarge the probability difference between the correct and incorrect classes. We added hyperparameters to CRL, thereby ensuring its value to be positive and that the update size of backpropagation is suitable for the CRL's fast convergence. To demonstrate the performance of CRL, we conducted experiments on general image classification tasks (CIFAR10/100, SVHN, ImageNet), the fine-grained image classification tasks (CUB200-2011 and Stanford Car), and the challenging face age estimation task (using Adience). Experimental results show the effectiveness and robustness of the proposed loss function on different deep convolutional neural network architectures and different image classification tasks.
In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is often not sufficient. We propose and study calibration measures for multi-class classification that generalize existing measures such as the expected calibration error, the maximum calibration error, and the maximum mean calibration error. We propose and evaluate empirically different consistent and unbiased estimators for a specific class of measures based on matrix-valued kernels. Importantly, these estimators can be interpreted as test statistics associated with well-defined bounds and approximations of the p-value under the null hypothesis that the model is calibrated, significantly improving the interpretability of calibration measures, which otherwise lack any meaningful unit or scale.
Contemporary datasets on tobacco consumption focus on one of two topics, either public health mentions and disease surveillance, or sentiment analysis on topical tobacco products and services. However, two primary considerations are not accounted for, the language of the demographic affected and a combination of the topics mentioned above in a fine-grained classification mechanism. In this paper, we create a dataset of 3144 tweets, which are selected based on the presence of colloquial slang related to smoking and analyze it based on the semantics of the tweet. Each class is created and annotated based on the content of the tweets such that further hierarchical methods can be easily applied. Further, we prove the efficacy of standard text classification methods on this dataset, by designing experiments which do both binary as well as multi-class classification. Our experiments tackle the identification of either a specific topic (such as tobacco product promotion), a general mention (cigarettes and related products) or a more fine-grained classification. This methodology paves the way for further analysis, such as understanding sentiment or style, which makes this dataset a vital contribution to both disease surveillance and tobacco use research.
Accurate localization of proteins from fluorescence microscopy images is challenging due to the inter-class similarities and intra-class disparities introducing grave concerns in addressing multi-class classification problems. Conventional machine learning-based image prediction pipelines rely heavily on pre-processing such as normalization and segmentation followed by hand-crafted feature extraction to identify useful, informative, and application-specific features. Here, we demonstrate that deep learning-based pipelines can effectively classify protein images from different datasets. We propose an end-to-end Protein Localization Convolutional Neural Network (PLCNN) that classifies protein images more accurately and reliably. PLCNN processes raw imagery without involving any pre-processing steps and produces outputs without any customization or parameter adjustment for a particular dataset. Experimental analysis is performed on five benchmark datasets. PLCNN consistently outperformed the existing state-of-the-art approaches from traditional machine learning and deep architectures. This study highlights the importance of deep learning for the analysis of fluorescence microscopy protein imagery. The proposed deep pipeline can better guide drug designing procedures in the pharmaceutical industry and open new avenues for researchers in computational biology and bioinformatics.
Semi-supervised learning (SSL) is effectively used for numerous classification problems, thanks to its ability to make use of abundant unlabeled data. The main assumption of various SSL algorithms is that the nearby points on the data manifold are likely to share a label. Graph-based SSL constructs a graph from point-cloud data as an approximation to the underlying manifold, followed by label inference. It is no surprise that the quality of the constructed graph in capturing the essential structure of the data is critical to the accuracy of the subsequent inference step [6]. How should one construct a graph from the input point-cloud data for graph-based SSL? In this work we introduce a new, parallel graph learning framework (called PG-learn) for the graph construction step of SSL. Our solution has two main ingredients: (1) a gradient-based optimization of the edge weights (more specifically, different kernel bandwidths in each dimension) based on a validation loss function, and (2) a parallel hyperparameter search algorithm with an adaptive resource allocation scheme. In essence, (1) allows us to search around a (random) initial hyperparameter configuration for a better one with lower validation loss. Since the search space of hyperparameters is huge for high-dimensional problems, (2) empowers our gradient-based search to go through as many different initial configurations as possible, where runs for relatively unpromising starting configurations are terminated early to allocate the time for others. As such, PG-learn is a carefully-designed hybrid of random and adaptive search. Through experiments on multi-class classification problems, we show that PG-learn significantly outperforms a variety of existing graph construction schemes in accuracy (per fixed time budget for hyperparameter tuning), and scales more effectively to high dimensional problems.
Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel matrix, and (ii) intractable inference due to the non-Gaussian likelihoods. Hence, various scalable GPCs have been proposed through (i) the sparse approximation built upon a small inducing set to reduce the time complexity; and (ii) the approximate inference to derive analytical evidence lower bound (ELBO). However, these scalable GPCs equipped with analytical ELBO are limited to specific likelihoods or additional assumptions. In this work, we present a unifying framework which accommodates scalable GPCs using various likelihoods. Analogous to GP regression (GPR), we introduce additive noises to augment the probability space for (i) the GPCs with step, (multinomial) probit and logit likelihoods via the internal variables; and particularly, (ii) the GPC using softmax likelihood via the noise variables themselves. This leads to unified scalable GPCs with analytical ELBO by using variational inference. Empirically, our GPCs showcase better results than state-of-the-art scalable GPCs for extensive binary/multi-class classification tasks with up to two million data points.
Different aspects of a clinical sample can be revealed by multiple types of omics data. Integrated analysis of multi-omics data provides a comprehensive view of patients, which has the potential to facilitate more accurate clinical decision making. However, omics data are normally high dimensional with large number of molecular features and relatively small number of available samples with clinical labels. The "dimensionality curse" makes it challenging to train a machine learning model using high dimensional omics data like DNA methylation and gene expression profiles. Here we propose an end-to-end deep learning model called OmiVAE to extract low dimensional features and classify samples from multi-omics data. OmiVAE combines the basic structure of variational autoencoders with a classification network to achieve task-oriented feature extraction and multi-class classification. The training procedure of OmiVAE is comprised of an unsupervised phase without the classifier and a supervised phase with the classifier. During the unsupervised phase, a hierarchical cluster structure of samples can be automatically formed without the need for labels. And in the supervised phase, OmiVAE achieved an average classification accuracy of 97.49% after 10-fold cross-validation among 33 tumour types and normal samples, which shows better performance than other existing methods. The OmiVAE model learned from multi-omics data outperformed that using only one type of omics data, which indicates that the complementary information from different omics datatypes provides useful insights for biomedical tasks like cancer classification.
Convolutional Neural Networks (CNN) have become state-of-the-art in the field of image classification. However, not everything is understood about their inner representations. This paper tackles the interpretability and explainability of the predictions of CNNs for multi-class classification problems. Specifically, we propose a novel visualization method of pixel-wise input attribution called Softmax-Gradient Layer-wise Relevance Propagation (SGLRP). The proposed model is a class discriminate extension to Deep Taylor Decomposition (DTD) using the gradient of softmax to back propagate the relevance of the output probability to the input image. Through qualitative and quantitative analysis, we demonstrate that SGLRP can successfully localize and attribute the regions on input images which contribute to a target object's classification. We show that the proposed method excels at discriminating the target objects class from the other possible objects in the images. We confirm that SGLRP performs better than existing Layer-wise Relevance Propagation (LRP) based methods and can help in the understanding of the decision process of CNNs.
Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes from a combination of several characteristics: a remarkable accuracy in a variety of tasks, a small number of parameters to tune, robustness with respect to features scaling, a reasonable computational cost for training and prediction, and their suitability in high-dimensional settings. The most commonly used RF variants however are "offline" algorithms, which require the availability of the whole dataset at once. In this paper, we introduce AMF, an online random forest algorithm based on Mondrian Forests. Using a variant of the Context Tree Weighting algorithm, we show that it is possible to efficiently perform an exact aggregation over all prunings of the trees; in particular, this enables to obtain a truly online parameter-free algorithm which is competitive with the optimal pruning of the Mondrian tree, and thus adaptive to the unknown regularity of the regression function. Numerical experiments show that AMF is competitive with respect to several strong baselines on a large number of datasets for multi-class classification.
Many applications of classification methods not only require high accuracy but also reliable estimation of predictive uncertainty. However, while many current classification frameworks, in particular deep neural networks, achieve high accuracy, they tend to incorrectly estimate uncertainty. In this paper, we propose a method that adjusts the confidence estimates of a general classifier such that they approach the probability of classifying correctly. In contrast to existing approaches, our calibration method employs a non-parametric representation using a latent Gaussian process, and is specifically designed for multi-class classification. It can be applied to any classifier that outputs confidence estimates and is not limited to neural networks. We also provide a theoretical analysis regarding the over- and underconfidence of a classifier and its relationship to calibration, as well as an empirical outlook for calibrated active learning. In experiments we show the universally strong performance of our method across different classifiers and benchmark data sets, in particular for state-of-the art neural network architectures.
Recent works have shown that stochastic gradient descent (SGD) achieves the fast convergence rates of full-batch gradient descent for over-parameterized models satisfying certain interpolation conditions. However, the step-size used in these works depends on unknown quantities and SGD's practical performance heavily relies on the choice of this step-size. We propose to use line-search techniques to automatically set the step-size when training models that can interpolate the data. In the interpolation setting, we prove that SGD with a stochastic variant of the classic Armijo line-search attains the deterministic convergence rates for both convex and strongly-convex functions. Under additional assumptions, SGD with Armijo line-search is shown to achieve fast convergence for non-convex functions. Furthermore, we show that stochastic extra-gradient with a Lipschitz line-search attains linear convergence for an important class of non-convex functions and saddle-point problems satisfying interpolation. To improve the proposed methods' practical performance, we give heuristics to use larger step-sizes and acceleration. We compare the proposed algorithms against numerous optimization methods on standard classification tasks using both kernel methods and deep networks. The proposed methods result in competitive performance across all models and datasets, while being robust to the precise choices of hyper-parameters. For multi-class classification using deep networks, SGD with Armijo line-search results in both faster convergence and better generalization.
While semi-supervised learning (SSL) algorithms provide an efficient way to make use of both labelled and unlabelled data, they generally struggle when the number of annotated samples is very small. In this work, we consider the problem of SSL multi-class classification with very few labelled instances. We introduce two key ideas. The first is a simple but effective one: we leverage the power of transfer learning among different tasks and self-supervision to initialize a good representation of the data without making use of any label. The second idea is a new algorithm for SSL that can exploit well such a pre-trained representation. The algorithm works by alternating two phases, one fitting the labelled points and one fitting the unlabelled ones, with carefully-controlled information flow between them. The benefits are greatly reducing overfitting of the labelled data and avoiding issue with balancing labelled and unlabelled losses during training. We show empirically that this method can successfully train competitive models with as few as 10 labelled data points per class. More in general, we show that the idea of bootstrapping features using self-supervised learning always improves SSL on standard benchmarks. We show that our algorithm works increasingly well compared to other methods when refining from other tasks or datasets.
Depth estimation is a traditional computer vision task, which plays a crucial role in understanding 3D scene geometry. Recently, deep-convolutional-neural-networks based methods have achieved promising results in the monocular depth estimation field. Specifically, the framework that combines the multi-scale features extracted by the dilated convolution based block (atrous spatial pyramid pooling, ASPP) has gained the significant improvement in the dense labeling task. However, the discretized and predefined dilation rates cannot capture the continuous context information that differs in diverse scenes and easily introduce the grid artifacts in depth estimation. In this paper, we propose an attention-based context aggregation network (ACAN) to tackle these difficulties. Based on the self-attention model, ACAN adaptively learns the task-specific similarities between pixels to model the context information. First, we recast the monocular depth estimation as a dense labeling multi-class classification problem. Then we propose a soft ordinal inference to transform the predicted probabilities to continuous depth values, which can reduce the discretization error (about 1% decrease in RMSE). Second, the proposed ACAN aggregates both the image-level and pixel-level context information for depth estimation, where the former expresses the statistical characteristic of the whole image and the latter extracts the long-range spatial dependencies for each pixel. Third, for further reducing the inconsistency between the RGB image and depth map, we construct an attention loss to minimize their information entropy. We evaluate on public monocular depth-estimation benchmark datasets (including NYU Depth V2, KITTI). The experiments demonstrate the superiority of our proposed ACAN and achieve the competitive results with the state of the arts.
Crowdsourcing has become widely used in supervised scenarios where training sets are scarce and difficult to obtain. Most crowdsourcing models in the literature assume labelers can provide answers to full questions. In classification contexts, full questions require a labeler to discern among all possible classes. Unfortunately, discernment is not always easy in realistic scenarios. Labelers may not be experts in differentiating all classes. In this work, we provide a full probabilistic model for a shorter type of queries. Our shorter queries only require "yes" or "no" responses. Our model estimates a joint posterior distribution of matrices related to labelers' confusions and the posterior probability of the class of every object. We developed an approximate inference approach, using Monte Carlo Sampling and Black Box Variational Inference, which provides the derivation of the necessary gradients. We built two realistic crowdsourcing scenarios to test our model. The first scenario queries for irregular astronomical time-series. The second scenario relies on the image classification of animals. We achieved results that are comparable with those of full query crowdsourcing. Furthermore, we show that modeling labelers' failures plays an important role in estimating true classes. Finally, we provide the community with two real datasets obtained from our crowdsourcing experiments. All our code is publicly available.
This work presents a new strategy for multi-class classification that requires no class-specific labels, but instead leverages pairwise similarity between examples, which is a weaker form of annotation. The proposed method, meta classification learning, optimizes a binary classifier for pairwise similarity prediction and through this process learns a multi-class classifier as a submodule. We formulate this approach, present a probabilistic graphical model for it, and derive a surprisingly simple loss function that can be used to learn neural network-based models. We then demonstrate that this same framework generalizes to the supervised, unsupervised cross-task, and semi-supervised settings. Our method is evaluated against state of the art in all three learning paradigms and shows a superior or comparable accuracy, providing evidence that learning multi-class classification without multi-class labels is a viable learning option.
We evaluate machine learning methods for event classification in the Active-Target Time Projection Chamber detector at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. An automated method to single out the desired reaction product would result in more accurate physics results as well as a faster analysis process. Binary and multi-class classification methods were tested on data produced by the $^{46}$Ar(p,p) experiment run at the NSCL in September 2015. We found a Convolutional Neural Network to be the most successful classifier of proton scattering events for transfer learning. Results from this investigation and recommendations for event classification in future experiments are presented.