Meta-learning One-class Classifiers with Eigenvalue Solvers for Supervised Anomaly Detection

Neural network-based anomaly detection methods have shown to achieve high performance. However, they require a large amount of training data for each task. We propose a neural network-based meta-learning method for supervised anomaly detection. The proposed method improves the anomaly detection performance on unseen tasks, which contains a few labeled normal and anomalous instances, by meta-training with various datasets. With a meta-learning framework, quick adaptation to each task and its effective backpropagation are important since the model is trained by the adaptation for each epoch. Our model enables them by formulating adaptation as a generalized eigenvalue problem with one-class classification; its global optimum solution is obtained, and the solver is differentiable. We experimentally demonstrate that the proposed method achieves better performance than existing anomaly detection and few-shot learning methods on various datasets.

Meta-Learning for Koopman Spectral Analysis with Short Time-series

Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find appropriate embedding functions. Although several neural network-based methods have been proposed for learning embedding functions, existing methods require long time-series for training neural networks. This limitation prohibits performing Koopman spectral analysis in applications where only short time-series are available. In this paper, we propose a meta-learning method for estimating embedding functions from unseen short time-series by exploiting knowledge learned from related but different time-series. With the proposed method, a representation of a given short time-series is obtained by a bidirectional LSTM for extracting its properties. The embedding function of the short time-series is modeled by a neural network that depends on the time-series representation. By sharing the LSTM and neural networks across multiple time-series, we can learn common knowledge from different time-series while modeling time-series-specific embedding functions with the time-series representation. Our model is trained such that the expected test prediction error is minimized with the episodic training framework. We experimentally demonstrate that the proposed method achieves better performance in terms of eigenvalue estimation and future prediction than existing methods.

Adversarial Training Makes Weight Loss Landscape Sharper in Logistic Regression

Adversarial training is actively studied for learning robust models against adversarial examples. A recent study finds that adversarially trained models degenerate generalization performance on adversarial examples when their weight loss landscape, which is loss changes with respect to weights, is sharp. Unfortunately, it has been experimentally shown that adversarial training sharpens the weight loss landscape, but this phenomenon has not been theoretically clarified. Therefore, we theoretically analyze this phenomenon in this paper. As a first step, this paper proves that adversarial training with the L2 norm constraints sharpens the weight loss landscape in the linear logistic regression model. Our analysis reveals that the sharpness of the weight loss landscape is caused by the noise aligned in the direction of increasing the loss, which is used in adversarial training. We theoretically and experimentally confirm that the weight loss landscape becomes sharper as the magnitude of the noise of adversarial training increases in the linear logistic regression model. Moreover, we experimentally confirm the same phenomena in ResNet18 with softmax as a more general case.

Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics

Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to find an appropriate lift function. Although several methods have been proposed for estimating a lift function based on neural networks, the existing methods train neural networks without spectral analysis. In this paper, we propose neural dynamic mode decomposition, in which neural networks are trained such that the forecast error is minimized when the dynamics is modeled based on spectral decomposition in the lifted space. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition, enabling end-to-end learning of Koopman spectral analysis. When information is available on the frequencies or the growth rates of the dynamics, the proposed method can exploit it as regularizers for training. We also propose an extension of our approach when observations are influenced by exogenous control time-series. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.

Learning Contextualised Cross-lingual Word Embeddings for Extremely Low-Resource Languages Using Parallel Corpora

We propose a new approach for learning contextualised cross-lingual word embeddings based only on a small parallel corpus (e.g. a few hundred sentence pairs). Our method obtains word embeddings via an LSTM-based encoder-decoder model that performs bidirectional translation and reconstruction of the input sentence. Through sharing model parameters among different languages, our model jointly trains the word embeddings in a common multilingual space. We also propose a simple method to combine word and subword embeddings to make use of orthographic similarities across different languages. We base our experiments on real-world data from endangered languages, namely Yongning Na, Shipibo-Konibo and Griko. Our experiments on bilingual lexicon induction and word alignment tasks show that our model outperforms existing methods by a large margin for most language pairs. These results demonstrate that, contrary to common belief, an encoder-decoder translation model is beneficial for learning cross-lingual representations, even in extremely low-resource scenarios.

Meta-Active Learning for Node Response Prediction in Graphs

Meta-learning is an important approach to improve machine learning performance with a limited number of observations for target tasks. However, when observations are unbalancedly obtained, it is difficult to improve the performance even with meta-learning methods. In this paper, we propose an active learning method for meta-learning on node response prediction tasks in attributed graphs, where nodes to observe are selected to improve performance with as few observed nodes as possible. With the proposed method, we use models based on graph convolutional neural networks for both predicting node responses and selecting nodes, by which we can predict responses and select nodes even for graphs with unseen response variables. The response prediction model is trained by minimizing the expected test error. The node selection model is trained by maximizing the expected error reduction with reinforcement learning. We demonstrate the effectiveness of the proposed method with 11 types of road congestion prediction tasks.

Few-shot Learning for Spatial Regression

We propose a few-shot learning method for spatial regression. Although Gaussian processes (GPs) have been successfully used for spatial regression, they require many observations in the target task to achieve a high predictive performance. Our model is trained using spatial datasets on various attributes in various regions, and predicts values on unseen attributes in unseen regions given a few observed data. With our model, a task representation is inferred from given small data using a neural network. Then, spatial values are predicted by neural networks with a GP framework, in which task-specific properties are controlled by the task representations. The GP framework allows us to analytically obtain predictions that are adapted to small data. By using the adapted predictions in the objective function, we can train our model efficiently and effectively so that the test predictive performance improves when adapted to newly given small data. In our experiments, we demonstrate that the proposed method achieves better predictive performance than existing meta-learning methods using spatial datasets.

Few-shot Learning for Time-series Forecasting

Time-series forecasting is important for many applications. Forecasting models are usually trained using time-series data in a specific target task. However, sufficient data in the target task might be unavailable, which leads to performance degradation. In this paper, we propose a few-shot learning method that forecasts a future value of a time-series in a target task given a few time-series in the target task. Our model is trained using time-series data in multiple training tasks that are different from target tasks. Our model uses a few time-series to build a forecasting function based on a recurrent neural network with an attention mechanism. With the attention mechanism, we can retrieve useful patterns in a small number of time-series for the current situation. Our model is trained by minimizing an expected test error of forecasting next timestep values. We demonstrate the effectiveness of the proposed method using 90 time-series datasets.

Gaussian Process Regression with Local Explanation

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various applications. However, in GPR, how the features of an input contribute to its prediction cannot be interpreted. Herein, we propose GPR with local explanation, which reveals the feature contributions to the prediction of each sample, while maintaining the predictive performance of GPR. In the proposed model, both the prediction and explanation for each sample are performed using an easy-to-interpret locally linear model. The weight vector of the locally linear model is assumed to be generated from multivariate Gaussian process priors. The hyperparameters of the proposed models are estimated by maximizing the marginal likelihood. For a new test sample, the proposed model can predict the values of its target variable and weight vector, as well as their uncertainties, in a closed form. Experimental results on various benchmark datasets verify that the proposed model can achieve predictive performance comparable to those of GPR and superior to that of existing interpretable models, and can achieve higher interpretability than them, both quantitatively and qualitatively.

Probabilistic Optimal Transport based on Collective Graphical Models

Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has been defined as the minimum cost to transport probability mass from one probability distribution to another. In this study, we propose a new framework in which OT is considered as a maximum a posteriori (MAP) solution of a probabilistic generative model. With the proposed framework, we show that OT with entropic regularization is equivalent to maximizing a posterior probability of a probabilistic model called Collective Graphical Model (CGM), which describes aggregated statistics of multiple samples generated from a graphical model. Interpreting OT as a MAP solution of a CGM has the following two advantages: (i) We can calculate the discrepancy between noisy histograms by modeling noise distributions. Since various distributions can be used for noise modeling, it is possible to select the noise distribution flexibly to suit the situation. (ii) We can construct a new method for interpolation between histograms, which is an important application of OT. The proposed method allows for intuitive modeling based on the probabilistic interpretations, and a simple and efficient estimation algorithm is available. Experiments using synthetic and real-world spatio-temporal population datasets show the effectiveness of the proposed interpolation method.