Bayesian hierarchical model (BHM) has been widely used in synthesizing information across subgroups. Identifying heterogeneity in the data and determining proper strength of borrow have long been central goals pursued by researchers. Because these two goals are interconnected, we must consider them together. This joint consideration presents two fundamental challenges: (1) How can we balance the trade-off between homogeneity within the cluster and information gain through borrowing? (2) How can we determine the borrowing strength dynamically in different clusters? To tackle challenges, first, we develop a theoretical framework for heterogeneity identification and dynamic information borrowing in BHM. Then, we propose two novel overlapping indices: the overlapping clustering index (OCI) for identifying the optimal clustering result and the overlapping borrowing index (OBI) for assigning proper borrowing strength to clusters. By incorporating these indices, we develop a new method BHMOI (Bayesian hierarchical model with overlapping indices). BHMOI includes a novel weighted K-Means clustering algorithm by maximizing OCI to obtain optimal clustering results, and embedding OBI into BHM for dynamically borrowing within clusters. BHMOI can achieve efficient and robust information borrowing with desirable properties. Examples and simulation studies are provided to demonstrate the effectiveness of BHMOI in heterogeneity identification and dynamic information borrowing.
相關內容
We investigate trade-offs in static and dynamic evaluation of hierarchical queries with arbitrary free variables. In the static setting, the trade-off is between the time to partially compute the query result and the delay needed to enumerate its tuples. In the dynamic setting, we additionally consider the time needed to update the query result under single-tuple inserts or deletes to the database. Our approach observes the degree of values in the database and uses different computation and maintenance strategies for high-degree (heavy) and low-degree (light) values. For the latter it partially computes the result, while for the former it computes enough information to allow for on-the-fly enumeration. We define the preprocessing time, the update time, and the enumeration delay as functions of the light/heavy threshold. By appropriately choosing this threshold, our approach recovers a number of prior results when restricted to hierarchical queries. We show that for a restricted class of hierarchical queries, our approach achieves worst-case optimal update time and enumeration delay conditioned on the Online Matrix-Vector Multiplication Conjecture.
The sparsity of Deep Neural Networks is well investigated to maximize the performance and reduce the size of overparameterized networks as possible. Existing methods focus on pruning parameters in the training process by using thresholds and metrics. Meanwhile, feature similarity between different layers has not been discussed sufficiently before, which could be rigorously proved to be highly correlated to the network sparsity in this paper. Inspired by interlayer feature similarity in overparameterized models, we investigate the intrinsic link between network sparsity and interlayer feature similarity. Specifically, we prove that reducing interlayer feature similarity based on Centered Kernel Alignment (CKA) improves the sparsity of the network by using information bottleneck theory. Applying such theory, we propose a plug-and-play CKA-based Sparsity Regularization for sparse network training, dubbed CKA-SR, which utilizes CKA to reduce feature similarity between layers and increase network sparsity. In other words, layers of our sparse network tend to have their own identity compared to each other. Experimentally, we plug the proposed CKA-SR into the training process of sparse network training methods and find that CKA-SR consistently improves the performance of several State-Of-The-Art sparse training methods, especially at extremely high sparsity. Code is included in the supplementary materials.
Simulations of biophysical systems are fundamental for studying physiological mechanisms and developing human machine interfaces. Whilst advanced numerical methods, such as finite element models, can excel in this task, they are extremely computationally expensive to use when generating a large number of simulations or simulating dynamic events with continuously changing structural parameters. We propose an architecture that uses a conditional generative model to interpolate between the numerical model states, dramatically lowering the modeling time while maintaining a high generation accuracy. As a demonstration of this concept, we present BioMime, a hybrid-structured generative model that enables an accurate, ultra-fast, and arbitrarily high temporal-resolution simulation of a specific biophysical system during dynamic changes. This methodology has wide applications in physiological and clinical research as well as in supporting data augmentation strategies for signal analysis, representing a computationally efficient and highly accurate model for biophysical simulations.
Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. In this application, we corroborate evidence for the recently proposed L\'evy flight model of decision-making and show how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method.
In this paper we present a layered approach for multi-agent control problem, decomposed into three stages, each building upon the results of the previous one. First, a high-level plan for a coarse abstraction of the system is computed, relying on parametric timed automata augmented with stopwatches as they allow to efficiently model simplified dynamics of such systems. In the second stage, the high-level plan, based on SMT-formulation, mainly handles the combinatorial aspects of the problem, provides a more dynamically accurate solution. These stages are collectively referred to as the SWA-SMT solver. They are correct by construction but lack a crucial feature: they cannot be executed in real time. To overcome this, we use SWA-SMT solutions as the initial training dataset for our last stage, which aims at obtaining a neural network control policy. We use reinforcement learning to train the policy, and show that the initial dataset is crucial for the overall success of the method.
Dialog policies, which determine a system's action based on the current state at each dialog turn, are crucial to the success of the dialog. In recent years, reinforcement learning (RL) has emerged as a promising option for dialog policy learning (DPL). In RL-based DPL, dialog policies are updated according to rewards. The manual construction of fine-grained rewards, such as state-action-based ones, to effectively guide the dialog policy is challenging in multi-domain task-oriented dialog scenarios with numerous state-action pair combinations. One way to estimate rewards from collected data is to train the reward estimator and dialog policy simultaneously using adversarial learning (AL). Although this method has demonstrated superior performance experimentally, it is fraught with the inherent problems of AL, such as mode collapse. This paper first identifies the role of AL in DPL through detailed analyses of the objective functions of dialog policy and reward estimator. Next, based on these analyses, we propose a method that eliminates AL from reward estimation and DPL while retaining its advantages. We evaluate our method using MultiWOZ, a multi-domain task-oriented dialog corpus.
Vast amount of data generated from networks of sensors, wearables, and the Internet of Things (IoT) devices underscores the need for advanced modeling techniques that leverage the spatio-temporal structure of decentralized data due to the need for edge computation and licensing (data access) issues. While federated learning (FL) has emerged as a framework for model training without requiring direct data sharing and exchange, effectively modeling the complex spatio-temporal dependencies to improve forecasting capabilities still remains an open problem. On the other hand, state-of-the-art spatio-temporal forecasting models assume unfettered access to the data, neglecting constraints on data sharing. To bridge this gap, we propose a federated spatio-temporal model -- Cross-Node Federated Graph Neural Network (CNFGNN) -- which explicitly encodes the underlying graph structure using graph neural network (GNN)-based architecture under the constraint of cross-node federated learning, which requires that data in a network of nodes is generated locally on each node and remains decentralized. CNFGNN operates by disentangling the temporal dynamics modeling on devices and spatial dynamics on the server, utilizing alternating optimization to reduce the communication cost, facilitating computations on the edge devices. Experiments on the traffic flow forecasting task show that CNFGNN achieves the best forecasting performance in both transductive and inductive learning settings with no extra computation cost on edge devices, while incurring modest communication cost.
Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.
Multimodal sentiment analysis is a very actively growing field of research. A promising area of opportunity in this field is to improve the multimodal fusion mechanism. We present a novel feature fusion strategy that proceeds in a hierarchical fashion, first fusing the modalities two in two and only then fusing all three modalities. On multimodal sentiment analysis of individual utterances, our strategy outperforms conventional concatenation of features by 1%, which amounts to 5% reduction in error rate. On utterance-level multimodal sentiment analysis of multi-utterance video clips, for which current state-of-the-art techniques incorporate contextual information from other utterances of the same clip, our hierarchical fusion gives up to 2.4% (almost 10% error rate reduction) over currently used concatenation. The implementation of our method is publicly available in the form of open-source code.
Recently, deep learning has achieved very promising results in visual object tracking. Deep neural networks in existing tracking methods require a lot of training data to learn a large number of parameters. However, training data is not sufficient for visual object tracking as annotations of a target object are only available in the first frame of a test sequence. In this paper, we propose to learn hierarchical features for visual object tracking by using tree structure based Recursive Neural Networks (RNN), which have fewer parameters than other deep neural networks, e.g. Convolutional Neural Networks (CNN). First, we learn RNN parameters to discriminate between the target object and background in the first frame of a test sequence. Tree structure over local patches of an exemplar region is randomly generated by using a bottom-up greedy search strategy. Given the learned RNN parameters, we create two dictionaries regarding target regions and corresponding local patches based on the learned hierarchical features from both top and leaf nodes of multiple random trees. In each of the subsequent frames, we conduct sparse dictionary coding on all candidates to select the best candidate as the new target location. In addition, we online update two dictionaries to handle appearance changes of target objects. Experimental results demonstrate that our feature learning algorithm can significantly improve tracking performance on benchmark datasets.
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