Latent Block Models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster numbers of Latent Block Models. Recent studies have constructed statistical-test-based methods for Stochastic Block Models, in which we assume that the observed matrix is a square symmetric matrix and that the cluster assignments are the same for rows and columns. In this paper, we develop a goodness-of-fit test for Latent Block Models, which tests whether an observed data matrix fits a given set of row and column cluster numbers, or it consists of more clusters in at least one direction of row and column. To construct the test method, we use a result from random matrix theory for a sample covariance matrix. We show experimentally the effectiveness of our proposed method, by showing the asymptotic behavior of the test statistic and the test accuracy.

As machine learning is increasingly used to make real-world decisions, recent research efforts aim to define and ensure fairness in algorithmic decision making. Existing methods often assume a fixed set of observable features to define individuals, but lack a discussion of certain features not being observed at test time. In this paper, we study fairness of naive Bayes classifiers, which allow partial observations. In particular, we introduce the notion of a discrimination pattern, which refers to an individual receiving different classifications depending on whether some sensitive attributes were observed. Then a model is considered fair if it has no such pattern. We propose an algorithm to discover and mine for discrimination patterns in a naive Bayes classifier, and show how to learn maximum-likelihood parameters subject to these fairness constraints. Our approach iteratively discovers and eliminates discrimination patterns until a fair model is learned. An empirical evaluation on three real-world datasets demonstrates that we can remove exponentially many discrimination patterns by only adding a small fraction of them as constraints.

We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous training examples if they are unlikely fall into certain classes. We construct our new maximum likelihood estimators with self-correction property, and prove that under some conditions, our estimators converge faster. Also we discuss the advantages of applying one of our estimator to a fully supervised learning problem. The proposed method has potential applicability in many areas, such as crowdsourcing, natural language processing and medical image analysis.

In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the bias of variational inference can be reduced by making the distribution of the likelihood ratio more concentrated, such as via averaging and variance reduction.

Deep neural networks have achieved great success in classification tasks during the last years. However, one major problem to the path towards artificial intelligence is the inability of neural networks to accurately detect novel class distributions and therefore, most of the classification algorithms proposed make the assumption that all classes are known prior to the training stage. In this work, we propose a methodology for training a neural network that allows it to efficiently detect novel class distributions without compromising much of its classification accuracy on the test examples of known classes. Experimental results on the CIFAR 100 and MiniImagenet data sets demonstrate the effectiveness of the proposed algorithm. The way this method was constructed also makes it suitable for training any classification algorithm that is based on Maximum Likelihood methods.

In this paper, we aim to solve for unsupervised domain adaptation of classifiers where we have access to label information for the source domain while these are not available for a target domain. While various methods have been proposed for solving these including adversarial discriminator based methods, most approaches have focused on the entire image based domain adaptation. In an image, there would be regions that can be adapted better, for instance, the foreground object may be similar in nature. To obtain such regions, we propose methods that consider the probabilistic certainty estimate of various regions and specify focus on these during classification for adaptation. We observe that just by incorporating the probabilistic certainty of the discriminator while training the classifier, we are able to obtain state of the art results on various datasets as compared against all the recent methods. We provide a thorough empirical analysis of the method by providing ablation analysis, statistical significance test, and visualization of the attention maps and t-SNE embeddings. These evaluations convincingly demonstrate the effectiveness of the proposed approach.

One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian learning approach to alleviate these two issues by modeling architecture parameters using hierarchical automatic relevance determination (HARD) priors. Unlike other NAS methods, we train the over-parameterized network for only one epoch then update the architecture. Impressively, this enabled us to find the architecture on CIFAR-10 within only 0.2 GPU days using a single GPU. Competitive performance can be also achieved by transferring to ImageNet. As a byproduct, our approach can be applied directly to compress convolutional neural networks by enforcing structural sparsity which achieves extremely sparse networks without accuracy deterioration.

Deep neural networks (DNNs) have achieved state-of-the-art performances in many important domains, including medical diagnosis, security, and autonomous driving. In these domains where safety is highly critical, an erroneous decision can result in serious consequences. While a perfect prediction accuracy is not always achievable, recent work on Bayesian deep networks shows that it is possible to know when DNNs are more likely to make mistakes. Knowing what DNNs do not know is desirable to increase the safety of deep learning technology in sensitive applications. Bayesian neural networks attempt to address this challenge. However, traditional approaches are computationally intractable and do not scale well to large, complex neural network architectures. In this paper, we develop a theoretical framework to approximate Bayesian inference for DNNs by imposing a Bernoulli distribution on the model weights. This method, called MC-DropConnect, gives us a tool to represent the model uncertainty with little change in the overall model structure or computational cost. We extensively validate the proposed algorithm on multiple network architectures and datasets for classification and semantic segmentation tasks. We also propose new metrics to quantify the uncertainty estimates. This enables an objective comparison between MC-DropConnect and prior approaches. Our empirical results demonstrate that the proposed framework yields significant improvement in both prediction accuracy and uncertainty estimation quality compared to the state of the art.

Clustering is used to find structure in unlabeled data by grouping similar objects together. Cluster analysis depends on the definition of similarity in the feature space. In this paper, we propose an Adaptive Nonparametric Variational Autoencoder (AdapVAE) to perform end-to-end feature learning from raw data jointly with cluster membership learning through a Nonparametric Bayesian modeling framework with deep neural networks. It has the advantage of avoiding pre-definition of similarity or feature engineering. Our model relaxes the constraint of fixing the number of clusters in advance by assigning a Dirichlet Process prior on the latent representation in a low-dimensional feature space. It can adaptively detect novel clusters when new data arrives based on a learned model from historical data in an online unsupervised learning setting. We develop a joint online variational inference algorithm to learn feature representations and cluster assignments via iteratively optimizing the evidence lower bound (ELBO). Our experimental results demonstrate the capacity of our modelling framework to learn the number of clusters automatically using data, the flexibility to detect novel clusters with emerging data adaptively, the ability of high quality reconstruction and generation of samples without supervised information and the improvement over state-of-the-art end-to-end clustering methods in terms of accuracy on both image and text corpora benchmark datasets.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density, and reduce the memory required during training by a factor of ten. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid gradient saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.