Unsupervised representation learning has succeeded with excellent results in many applications. It is an especially powerful tool to learn a good representation of environments with partial or noisy observations. In partially observable domains it is important for the representation to encode a belief state, a sufficient statistic of the observations seen so far. In this paper, we investigate whether it is possible to learn such a belief representation using modern neural architectures. Specifically, we focus on one-step frame prediction and two variants of contrastive predictive coding (CPC) as the objective functions to learn the representations. To evaluate these learned representations, we test how well they can predict various pieces of information about the underlying state of the environment, e.g., position of the agent in a 3D maze. We show that all three methods are able to learn belief representations of the environment, they encode not only the state information, but also its uncertainty, a crucial aspect of belief states. We also find that for CPC multi-step predictions and action-conditioning are critical for accurate belief representations in visually complex environments. The ability of neural representations to capture the belief information has the potential to spur new advances for learning and planning in partially observable domains, where leveraging uncertainty is essential for optimal decision making.

Abstract--Support vector data description (SVDD) is a popular anomaly detection technique. The SVDD classifier partitions the whole data space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classifier requires a kernel function, for which the Gaussian kernel is a common choice. The Gaussian kernel has a bandwidth parameter, and it is important to set the value of this parameter correctly for good results. A small bandwidth leads to overfitting such that the resulting SVDD classifier overestimates the number of anomalies, whereas a large bandwidth leads to underfitting and an inability to detect many anomalies. In this paper, we present a new unsupervised method for selecting the Gaussian kernel bandwidth. Our method, which exploits the lowrank representationof the kernel matrix to suggest a kernel bandwidth value, is competitive with existing bandwidth selection methods. I. INTRODUCTION Support vector data description (SVDD) is a machine learning techniquethat is used for single-class classification and anomaly detection.

Understanding and accurately predicting within-field spatial variability of crop yield play a key role in site-specific management of crop inputs such as irrigation water and fertilizer for optimized crop production. However, such a task is challenged by the complex interaction between crop growth and environmental and managerial factors, such as climate, soil conditions, tillage, and irrigation. In this paper, we present a novel Spatial-temporal Multi-Task Learning algorithms for within-field crop yield prediction in west Texas from 2001 to 2003. This algorithm integrates multiple heterogeneous data sources to learn different features simultaneously, and to aggregate spatial-temporal features by introducing a weighted regularizer to the loss functions. Our comprehensive experimental results consistently outperform the results of other conventional methods, and suggest a promising approach, which improves the landscape of crop prediction research fields.

Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provides such an indicator for the model confidence. However, this measure is only valid if the covariance function and its hyperparameters fit the underlying data generating process. In this paper, we derive an upper bound for the mean square prediction error of misspecified Gaussian process models based on a pseudo-concave optimization problem. We present application scenarios and a simulation to compare the derived upper bound with the true mean square error.

Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features. Specifically, given a dataset and metric of interest, the goal is to return a function (or multiple functions) that 1) is robust to adversarial perturbations, and 2) has significant variation across the datapoints. We establish strong connections between adversarially robust features and a natural spectral property of the geometry of the dataset and metric of interest. This connection can be leveraged to provide both robust features, and a lower bound on the robustness of any function that has significant variance across the dataset. Finally, we provide empirical evidence that the adversarially robust features given by this spectral approach can be fruitfully leveraged to learn a robust (and accurate) model.

Gaussian processes provide a flexible framework for forecasting, removing noise, and interpreting long temporal datasets. State space modelling (Kalman filtering) enables these non-parametric models to be deployed on long datasets by reducing the complexity to linear in the number of data points. The complexity is still cubic in the state dimension $m$ which is an impediment to practical application. In certain special cases (Gaussian likelihood, regular spacing) the GP posterior will reach a steady posterior state when the data are very long. We leverage this and formulate an inference scheme for GPs with general likelihoods, where inference is based on single-sweep EP (assumed density filtering). The infinite-horizon model tackles the cubic cost in the state dimensionality and reduces the cost in the state dimension $m$ to $\mathcal{O}(m^2)$ per data point. The model is extended to online-learning of hyperparameters. We show examples for large finite-length modelling problems, and present how the method runs in real-time on a smartphone on a continuous data stream updated at 100~Hz.

The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we propose a highly scalable sampling based algorithm that clusters the entire data via first spectral clustering of a small random sample followed by classifying or labeling the remaining out of sample points. The key idea is that this random subset borrows information across the entire data set and that the problem of clustering points can be replaced with the more efficient and robust problem of "clustering sub-clusters". We provide theoretical guarantees for our procedure. The numerical results indicate we outperform other state-of-the-art subspace clustering algorithms with respect to accuracy and speed.

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks.

In this paper, we perform registration of noisy curves. We provide an appropriate model in estimating the rotation and scaling parameters to adjust a set of curves through a M-estimation procedure. We prove the consistency and the asymptotic normality of our estimators. Numerical simulation and a real life aeronautic example are given to illustrate our methodology.

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately, a "one-size-fits-all" solution is unattainable, as different analytical tasks may require different attention to global or local graph features. We develop SGR, the first, to our knowledge, method for learning graph representations in a self-supervised manner. Grounded on spectral graph analysis, SGR seamlessly combines all aforementioned desirable properties. In extensive experiments, we show how our approach works on large graph collections, facilitates self-supervised representation learning across a variety of application domains, and performs competitively to state-of-the-art methods without re-training.