Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings

The optimization of high-dimensional black-box functions is a challenging problem. When a low-dimensional linear embedding structure can be assumed, existing Bayesian optimization (BO) methods often transform the original problem into optimization in a low-dimensional space. They exploit the low-dimensional structure and reduce the computational burden. However, we reveal that this approach could be limited or inefficient in exploring the high-dimensional space mainly due to the biased reconstruction of the high-dimensional queries from the low-dimensional queries. In this paper, we investigate a simple alternative approach: tackling the problem in the original high-dimensional space using the information from the learned low-dimensional structure. We provide a theoretical analysis of the exploration ability. Furthermore, we show that our method is applicable to batch optimization problems with thousands of dimensions without any computational difficulty. We demonstrate the effectiveness of our method on high-dimensional benchmarks and a real-world function.

Active Learning for Regression with Aggregated Outputs

Due to the privacy protection or the difficulty of data collection, we cannot observe individual outputs for each instance, but we can observe aggregated outputs that are summed over multiple instances in a set in some real-world applications. To reduce the labeling cost for training regression models for such aggregated data, we propose an active learning method that sequentially selects sets to be labeled to improve the predictive performance with fewer labeled sets. For the selection measurement, the proposed method uses the mutual information, which quantifies the reduction of the uncertainty of the model parameters by observing the aggregated output. With Bayesian linear basis functions for modeling outputs given an input, which include approximated Gaussian processes and neural networks, we can efficiently calculate the mutual information in a closed form. With the experiments using various datasets, we demonstrate that the proposed method achieves better predictive performance with fewer labeled sets than existing methods.

Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces

We propose a data-driven method for controlling the frequency and convergence rate of black-box nonlinear dynamical systems based on the Koopman operator theory. With the proposed method, a policy network is trained such that the eigenvalues of a Koopman operator of controlled dynamics are close to the target eigenvalues. The policy network consists of a neural network to find a Koopman invariant subspace, and a pole placement module to adjust the eigenvalues of the Koopman operator. Since the policy network is differentiable, we can train it in an end-to-end fashion using reinforcement learning. We demonstrate that the proposed method achieves better performance than model-free reinforcement learning and model-based control with system identification.

Predicting Opinion Dynamics via Sociologically-Informed Neural Networks

Opinion formation and propagation are crucial phenomena in social networks and have been extensively studied across several disciplines. Traditionally, theoretical models of opinion dynamics have been proposed to describe the interactions between individuals (i.e., social interaction) and their impact on the evolution of collective opinions. Although these models can incorporate sociological and psychological knowledge on the mechanisms of social interaction, they demand extensive calibration with real data to make reliable predictions, requiring much time and effort. Recently, the widespread use of social media platforms provides new paradigms to learn deep learning models from a large volume of social media data. However, these methods ignore any scientific knowledge about the mechanism of social interaction. In this work, we present the first hybrid method called Sociologically-Informed Neural Network (SINN), which integrates theoretical models and social media data by transporting the concepts of physics-informed neural networks (PINNs) from natural science (i.e., physics) into social science (i.e., sociology and social psychology). In particular, we recast theoretical models as ordinary differential equations (ODEs). Then we train a neural network that simultaneously approximates the data and conforms to the ODEs that represent the social scientific knowledge. In addition, we extend PINNs by integrating matrix factorization and a language model to incorporate rich side information (e.g., user profiles) and structural knowledge (e.g., cluster structure of the social interaction network). Moreover, we develop an end-to-end training procedure for SINN, which involves Gumbel-Softmax approximation to include stochastic mechanisms of social interaction. Extensive experiments on real-world and synthetic datasets show SINN outperforms six baseline methods in predicting opinion dynamics.

Aggregated Multi-output Gaussian Processes with Knowledge Transfer Across Domains

Aggregate data often appear in various fields such as socio-economics and public security. The aggregate data are associated not with points but with supports (e.g., spatial regions in a city). Since the supports may have various granularities depending on attributes (e.g., poverty rate and crime rate), modeling such data is not straightforward. This article offers a multi-output Gaussian process (MoGP) model that infers functions for attributes using multiple aggregate datasets of respective granularities. In the proposed model, the function for each attribute is assumed to be a dependent GP modeled as a linear mixing of independent latent GPs. We design an observation model with an aggregation process for each attribute; the process is an integral of the GP over the corresponding support. We also introduce a prior distribution of the mixing weights, which allows a knowledge transfer across domains (e.g., cities) by sharing the prior. This is advantageous in such a situation where the spatially aggregated dataset in a city is too coarse to interpolate; the proposed model can still make accurate predictions of attributes by utilizing aggregate datasets in other cities. The inference of the proposed model is based on variational Bayes, which enables one to learn the model parameters using the aggregate datasets from multiple domains. The experiments demonstrate that the proposed model outperforms in the task of refining coarse-grained aggregate data on real-world datasets: Time series of air pollutants in Beijing and various kinds of spatial datasets from New York City and Chicago.

Meta-learning for Out-of-Distribution Detection via Density Estimation in Latent Space

Many neural network-based out-of-distribution (OoD) detection methods have been proposed. However, they require many training data for each target task. We propose a simple yet effective meta-learning method to detect OoD with small in-distribution data in a target task. With the proposed method, the OoD detection is performed by density estimation in a latent space. A neural network shared among all tasks is used to flexibly map instances in the original space to the latent space. The neural network is meta-learned such that the expected OoD detection performance is improved by using various tasks that are different from the target tasks. This meta-learning procedure enables us to obtain appropriate representations in the latent space for OoD detection. For density estimation, we use a Gaussian mixture model (GMM) with full covariance for each class. We can adapt the GMM parameters to in-distribution data in each task in a closed form by maximizing the likelihood. Since the closed form solution is differentiable, we can meta-learn the neural network efficiently with a stochastic gradient descent method by incorporating the solution into the meta-learning objective function. In experiments using six datasets, we demonstrate that the proposed method achieves better performance than existing meta-learning and OoD detection methods.

Excess risk analysis for epistemic uncertainty with application to variational inference

We analyze the epistemic uncertainty (EU) of supervised learning in Bayesian inference by focusing on the excess risk. Existing analysis is limited to the Bayesian setting, which assumes a correct model and exact Bayesian posterior distribution. Thus we cannot apply the existing theory to modern Bayesian algorithms, such as variational inference. To address this, we present a novel EU analysis in the frequentist setting, where data is generated from an unknown distribution. We show a relation between the generalization ability and the widely used EU measurements, such as the variance and entropy of the predictive distribution. Then we show their convergence behaviors theoretically. Finally, we propose new variational inference that directly controls the prediction and EU evaluation performances based on the PAC-Bayesian theory. Numerical experiments show that our algorithm significantly improves the EU evaluation over the existing methods.

Tight integration of neural- and clustering-based diarization through deep unfolding of infinite Gaussian mixture model

Speaker diarization has been investigated extensively as an important central task for meeting analysis. Recent trend shows that integration of end-to-end neural (EEND)-and clustering-based diarization is a promising approach to handle realistic conversational data containing overlapped speech with an arbitrarily large number of speakers, and achieved state-of-the-art results on various tasks. However, the approaches proposed so far have not realized {\it tight} integration yet, because the clustering employed therein was not optimal in any sense for clustering the speaker embeddings estimated by the EEND module. To address this problem, this paper introduces a {\it trainable} clustering algorithm into the integration framework, by deep-unfolding a non-parametric Bayesian model called the infinite Gaussian mixture model (iGMM). Specifically, the speaker embeddings are optimized during training such that it better fits iGMM clustering, based on a novel clustering loss based on Adjusted Rand Index (ARI). Experimental results based on CALLHOME data show that the proposed approach outperforms the conventional approach in terms of diarization error rate (DER), especially by substantially reducing speaker confusion errors, that indeed reflects the effectiveness of the proposed iGMM integration.

Training Deep Models to be Explained with Fewer Examples

Although deep models achieve high predictive performance, it is difficult for humans to understand the predictions they made. Explainability is important for real-world applications to justify their reliability. Many example-based explanation methods have been proposed, such as representer point selection, where an explanation model defined by a set of training examples is used for explaining a prediction model. For improving the interpretability, reducing the number of examples in the explanation model is important. However, the explanations with fewer examples can be unfaithful since it is difficult to approximate prediction models well by such example-based explanation models. The unfaithful explanations mean that the predictions by the explainable model are different from those by the prediction model. We propose a method for training deep models such that their predictions are faithfully explained by explanation models with a small number of examples. We train the prediction and explanation models simultaneously with a sparse regularizer for reducing the number of examples. The proposed method can be incorporated into any neural network-based prediction models. Experiments using several datasets demonstrate that the proposed method improves faithfulness while keeping the predictive performance.

Evacuation Shelter Scheduling Problem

Evacuation shelters, which are urgently required during natural disasters, are designed to minimize the burden of evacuation on human survivors. However, the larger the scale of the disaster, the more costly it becomes to operate shelters. When the number of evacuees decreases, the operation costs can be reduced by moving the remaining evacuees to other shelters and closing shelters as quickly as possible. On the other hand, relocation between shelters imposes a huge emotional burden on evacuees. In this study, we formulate the "Evacuation Shelter Scheduling Problem," which allocates evacuees to shelters in such a way to minimize the movement costs of the evacuees and the operation costs of the shelters. Since it is difficult to solve this quadratic programming problem directly, we show its transformation into a 0-1 integer programming problem. In addition, such a formulation struggles to calculate the burden of relocating them from historical data because no payments are actually made. To solve this issue, we propose a method that estimates movement costs based on the numbers of evacuees and shelters during an actual disaster. Simulation experiments with records from the Kobe earthquake (Great Hanshin-Awaji Earthquake) showed that our proposed method reduced operation costs by 33.7 million dollars: 32%.