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Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables ($p$) diverges as the number of serially dependent observations ($n$) increases. In this paper, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate the number of functional factors and the factor loadings, we propose a fully functional estimation procedure based on an eigenanalysis for a nonnegative definite matrix. Our proposal involves a weight matrix to improve the estimation efficiency and tackle the issue of heterogeneity, the rationality of which is illustrated by formulating the estimation from a novel regression perspective. Asymptotic properties of the proposed method are studied when $p$ diverges at some polynomial rate as $n$ increases. To provide a parsimonious model and enhance interpretability for near-zero factor loadings, we impose sparsity assumptions on the factor loading space and then develop a regularized estimation procedure with theoretical guarantees when $p$ grows exponentially fast relative to $n.$ Finally, we demonstrate that our proposed estimators significantly outperform the competing methods through both simulations and applications to a U.K. temperature dataset and a Japanese mortality dataset.

Inferential models (IMs) are data-dependent, probability-like structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference, and on establishing a validity property that ensures the IM is reliable in a specific sense. The present paper develops an IM framework for decision problems and, in particular, investigates the decision-theoretic implications of the aforementioned validity property. I show that a valid IM's assessment of an action's quality, defined by a Choquet integral, will not be too optimistic compared to that of an oracle. This ensures that a valid IM tends not to favor actions that the oracle doesn't also favor, hence a valid IM is reliable for decision-making too. In a certain special class of structured statistical models, further connections can be made between the valid IM's favored actions and those favored by other more familiar frameworks, from which certain optimality conclusions can be drawn. An important step in these decision-theoretic developments is a characterization of the valid IM's credal set in terms of confidence distributions, which may be of independent interest.

Waves of misery is a phenomenon where spikes of many node splits occur over short periods of time in tree indexes. Waves of misery negatively affect the performance of tree indexes in insertion-heavy workloads.Waves of misery have been first observed in the context of the B-tree, where these waves cause unpredictable index performance. In particular, the performance of search and index-update operations deteriorate when a wave of misery takes place, but is more predictable between the waves. This paper investigates the presence or lack of waves of misery in several R-tree variants, and studies the extent of which these waves impact the performance of each variant. Interestingly, although having poorer query performance, the Linear and Quadratic R-trees are found to be more resilient to waves of misery than both the Hilbert and R*-trees. This paper presents several techniques to reduce the impact in performance of the waves of misery for the Hilbert and R*-trees. One way to eliminate waves of misery is to force node splits to take place at regular times before nodes become full to achieve deterministic performance. The other way is that upon splitting a node, do not split it evenly but rather at different node utilization factors. This allows leaf nodes not to fill at the same pace. We study the impact of two new techniques to mitigate waves of misery after the tree index has been constructed, namely Regular Elective Splits (RES, for short) and Unequal Random Splits (URS, for short). Our experimental investigation highlights the trade-offs in performance of the introduced techniques and the pros and cons of each technique.

Tree ensemble methods such as random forests [Breiman, 2001] are very popular to handle high-dimensional tabular data sets, notably because of their good predictive accuracy. However, when machine learning is used for decision-making problems, settling for the best predictive procedures may not be reasonable since enlightened decisions require an in-depth comprehension of the algorithm prediction process. Unfortunately, random forests are not intrinsically interpretable since their prediction results from averaging several hundreds of decision trees. A classic approach to gain knowledge on this so-called black-box algorithm is to compute variable importances, that are employed to assess the predictive impact of each input variable. Variable importances are then used to rank or select variables and thus play a great role in data analysis. Nevertheless, there is no justification to use random forest variable importances in such way: we do not even know what these quantities estimate. In this paper, we analyze one of the two well-known random forest variable importances, the Mean Decrease Impurity (MDI). We prove that if input variables are independent and in absence of interactions, MDI provides a variance decomposition of the output, where the contribution of each variable is clearly identified. We also study models exhibiting dependence between input variables or interaction, for which the variable importance is intrinsically ill-defined. Our analysis shows that there may exist some benefits to use a forest compared to a single tree.

Imitation learning enables agents to reuse and adapt the hard-won expertise of others, offering a solution to several key challenges in learning behavior. Although it is easy to observe behavior in the real-world, the underlying actions may not be accessible. We present a new method for imitation solely from observations that achieves comparable performance to experts on challenging continuous control tasks while also exhibiting robustness in the presence of observations unrelated to the task. Our method, which we call FORM (for "Future Observation Reward Model") is derived from an inverse RL objective and imitates using a model of expert behavior learned by generative modelling of the expert's observations, without needing ground truth actions. We show that FORM performs comparably to a strong baseline IRL method (GAIL) on the DeepMind Control Suite benchmark, while outperforming GAIL in the presence of task-irrelevant features.

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from which exponentially many sub-networks can be sampled and efficiently evaluated. These methods enjoy great advantages in terms of computational costs, but the sampled sub-networks are not guaranteed to be estimated precisely unless an individual training process is taken. This paper owes such inaccuracy to the inevitable mismatch between assembled network layers, so that there is a random error term added to each estimation. We alleviate this issue by training a graph convolutional network to fit the performance of sampled sub-networks so that the impact of random errors becomes minimal. With this strategy, we achieve a higher rank correlation coefficient in the selected set of candidates, which consequently leads to better performance of the final architecture. In addition, our approach also enjoys the flexibility of being used under different hardware constraints, since the graph convolutional network has provided an efficient lookup table of the performance of architectures in the entire search space.

The problem of Approximate Nearest Neighbor (ANN) search is fundamental in computer science and has benefited from significant progress in the past couple of decades. However, most work has been devoted to pointsets whereas complex shapes have not been sufficiently treated. Here, we focus on distance functions between discretized curves in Euclidean space: they appear in a wide range of applications, from road segments to time-series in general dimension. For $\ell_p$-products of Euclidean metrics, for any $p$, we design simple and efficient data structures for ANN, based on randomized projections, which are of independent interest. They serve to solve proximity problems under a notion of distance between discretized curves, which generalizes both discrete Fr\'echet and Dynamic Time Warping distances. These are the most popular and practical approaches to comparing such curves. We offer the first data structures and query algorithms for ANN with arbitrarily good approximation factor, at the expense of increasing space usage and preprocessing time over existing methods. Query time complexity is comparable or significantly improved by our algorithms, our algorithm is especially efficient when the length of the curves is bounded.

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.

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict "em what drugs are likely to target proteins involved with both diseases X and Y?" -- a query that requires reasoning about all possible proteins that {\em might} interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.

Machine reading comprehension with unanswerable questions aims to abstain from answering when no answer can be inferred. In addition to extract answers, previous works usually predict an additional "no-answer" probability to detect unanswerable cases. However, they fail to validate the answerability of the question by verifying the legitimacy of the predicted answer. To address this problem, we propose a novel read-then-verify system, which not only utilizes a neural reader to extract candidate answers and produce no-answer probabilities, but also leverages an answer verifier to decide whether the predicted answer is entailed by the input snippets. Moreover, we introduce two auxiliary losses to help the reader better handle answer extraction as well as no-answer detection, and investigate three different architectures for the answer verifier. Our experiments on the SQuAD 2.0 dataset show that our system achieves a score of 74.2 F1 on the test set, achieving state-of-the-art results at the time of submission (Aug. 28th, 2018).