Bayesian hierarchical mixture clustering (BHMC) is an interesting model that improves on the traditional Bayesian hierarchical clustering approaches. Regarding the parent-to-node diffusion in the generative process, BHMC replaces the conventional Gaussian-to-Gaussian (G2G) kernels with a Hierarchical Dirichlet Process Mixture Model (HDPMM). However, the drawback of the BHMC lies in that it might obtain comparatively high nodal variance in the higher levels (i.e., those closer to the root node). This can be interpreted as that the separation between the nodes, in particular those in the higher levels, might be weak. Attempting to overcome this drawback, we consider a recent inferential framework named posterior regularization, which facilitates a simple manner to impose extra constraints on a Bayesian model to address some weakness of the original model. Hence, to enhance the separation of clusters, we apply posterior regularization to impose max-margin constraints on the nodes at every level of the hierarchy. In this paper, we illustrate how the framework integrates with the BHMC and achieves the desired improvements over the original model.
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The expense of acquiring labels in large-scale statistical machine learning makes partially and weakly-labeled data attractive, though it is not always apparent how to leverage such data for model fitting or validation. We present a methodology to bridge the gap between partial supervision and validation, developing a conformal prediction framework to provide valid predictive confidence sets -- sets that cover a true label with a prescribed probability, independent of the underlying distribution -- using weakly labeled data. To do so, we introduce a (necessary) new notion of coverage and predictive validity, then develop several application scenarios, providing efficient algorithms for classification and several large-scale structured prediction problems. We corroborate the hypothesis that the new coverage definition allows for tighter and more informative (but valid) confidence sets through several experiments.
The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This generalization allows for a larger degree of flexibility in the incorporation of prior knowledge over the set of models. In this setting, the interplay of the regularization parameter, the reference measure, the risk function, and the empirical risk induced by the solution of the ERM-RER problem is characterized. This characterization yields necessary and sufficient conditions for the existence of a regularization parameter that achieves an arbitrarily small empirical risk with arbitrarily high probability. The sensitivity of the expected empirical risk to deviations from the solution of the ERM-RER problem is studied. The sensitivity is then used to provide upper and lower bounds on the expected empirical risk. Moreover, it is shown that the expectation of the sensitivity is upper bounded, up to a constant factor, by the square root of the lautum information between the models and the datasets.
The Tree Augmented Naive Bayes (TAN) classifier is a type of probabilistic graphical model that constructs a single-parent dependency tree to estimate the distribution of the data. In this work, we propose two novel Hierarchical dependency-based Tree Augmented Naive Bayes algorithms, i.e. Hie-TAN and Hie-TAN-Lite. Both methods exploit the pre-defined parent-child (generalisation-specialisation) relationships between features as a type of constraint to learn the tree representation of dependencies among features, whilst the latter further eliminates the hierarchical redundancy during the classifier learning stage. The experimental results showed that Hie-TAN successfully obtained better predictive performance than several other hierarchical dependency constrained classification algorithms, and its predictive performance was further improved by eliminating the hierarchical redundancy, as suggested by the higher accuracy obtained by Hie-TAN-Lite.
Transformers are state-of-the-art in a wide range of NLP tasks and have also been applied to many real-world products. Understanding the reliability and certainty of transformer model predictions is crucial for building trustable machine learning applications, e.g., medical diagnosis. Although many recent transformer extensions have been proposed, the study of the uncertainty estimation of transformer models is under-explored. In this work, we propose a novel way to enable transformers to have the capability of uncertainty estimation and, meanwhile, retain the original predictive performance. This is achieved by learning a hierarchical stochastic self-attention that attends to values and a set of learnable centroids, respectively. Then new attention heads are formed with a mixture of sampled centroids using the Gumbel-Softmax trick. We theoretically show that the self-attention approximation by sampling from a Gumbel distribution is upper bounded. We empirically evaluate our model on two text classification tasks with both in-domain (ID) and out-of-domain (OOD) datasets. The experimental results demonstrate that our approach: (1) achieves the best predictive performance and uncertainty trade-off among compared methods; (2) exhibits very competitive (in most cases, improved) predictive performance on ID datasets; (3) is on par with Monte Carlo dropout and ensemble methods in uncertainty estimation on OOD datasets.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component.
Categorizing documents into a given label hierarchy is intuitively appealing due to the ubiquity of hierarchical topic structures in massive text corpora. Although related studies have achieved satisfying performance in fully supervised hierarchical document classification, they usually require massive human-annotated training data and only utilize text information. However, in many domains, (1) annotations are quite expensive where very few training samples can be acquired; (2) documents are accompanied by metadata information. Hence, this paper studies how to integrate the label hierarchy, metadata, and text signals for document categorization under weak supervision. We develop HiMeCat, an embedding-based generative framework for our task. Specifically, we propose a novel joint representation learning module that allows simultaneous modeling of category dependencies, metadata information and textual semantics, and we introduce a data augmentation module that hierarchically synthesizes training documents to complement the original, small-scale training set. Our experiments demonstrate a consistent improvement of HiMeCat over competitive baselines and validate the contribution of our representation learning and data augmentation modules.
When the federated learning is adopted among competitive agents with siloed datasets, agents are self-interested and participate only if they are fairly rewarded. To encourage the application of federated learning, this paper employs a management strategy, i.e., more contributions should lead to more rewards. We propose a novel hierarchically fair federated learning (HFFL) framework. Under this framework, agents are rewarded in proportion to their pre-negotiated contribution levels. HFFL+ extends this to incorporate heterogeneous models. Theoretical analysis and empirical evaluation on several datasets confirm the efficacy of our frameworks in upholding fairness and thus facilitating federated learning in the competitive settings.
We present a new clustering method in the form of a single clustering equation that is able to directly discover groupings in the data. The main proposition is that the first neighbor of each sample is all one needs to discover large chains and finding the groups in the data. In contrast to most existing clustering algorithms our method does not require any hyper-parameters, distance thresholds and/or the need to specify the number of clusters. The proposed algorithm belongs to the family of hierarchical agglomerative methods. The technique has a very low computational overhead, is easily scalable and applicable to large practical problems. Evaluation on well known datasets from different domains ranging between 1077 and 8.1 million samples shows substantial performance gains when compared to the existing clustering techniques.
Videos are a rich source of high-dimensional structured data, with a wide range of interacting components at varying levels of granularity. In order to improve understanding of unconstrained internet videos, it is important to consider the role of labels at separate levels of abstraction. In this paper, we consider the use of the Bidirectional Inference Neural Network (BINN) for performing graph-based inference in label space for the task of video classification. We take advantage of the inherent hierarchy between labels at increasing granularity. The BINN is evaluated on the first and second release of the YouTube-8M large scale multilabel video dataset. Our results demonstrate the effectiveness of BINN, achieving significant improvements against baseline models.
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