We present an active learning strategy for training parametric models of distance metrics, given triplet-based similarity assessments: object $x_i$ is more similar to object $x_j$ than to $x_k$. In contrast to prior work on class-based learning, where the fundamental goal is classification and any implicit or explicit metric is binary, we focus on {\em perceptual} metrics that express the {\em degree} of (dis)similarity between objects. We find that standard active learning approaches degrade when annotations are requested for {\em batches} of triplets at a time: our studies suggest that correlation among triplets is responsible. In this work, we propose a novel method to {\em decorrelate} batches of triplets, that jointly balances informativeness and diversity while decoupling the choice of heuristic for each criterion. Experiments indicate our method is general, adaptable, and outperforms the state-of-the-art.

Developments in Brain Computer Interfaces (BCIs) are empowering those with severe physical afflictions through their use in assistive systems. Common methods of achieving this is via Motor Imagery (MI), which maps brain signals to code for certain commands. Electroencephalogram (EEG) is preferred for recording brain signal data on account of it being non-invasive. Despite their potential utility, MI-BCI systems are yet confined to research labs. A major cause for this is lack of robustness of such systems. As hypothesized by two teams during Cybathlon 2016, a particular source of the system's vulnerability is the sharp change in the subject's state of emotional arousal. This work aims towards making MI-BCI systems resilient to such emotional perturbations. To do so, subjects are exposed to high and low arousal-inducing virtual reality (VR) environments before recording EEG data. The advent of COVID-19 compelled us to modify our methodology. Instead of training machine learning algorithms to classify emotional arousal, we opt for classifying subjects that serve as proxy for each state. Additionally, MI models are trained for each subject instead of each arousal state. As training subjects to use MI-BCI can be an arduous and time-consuming process, reducing this variability and increasing robustness can considerably accelerate the acceptance and adoption of assistive technologies powered by BCI.

This paper uses the peridynamic theory, which is well-suited to crack studies, to predict the crack patterns in a moving disk and classify them according to the modes and finally perform regression analysis. In that way, the crack patterns are obtained according to each mode by Molecular Dynamic (MD) simulation using the peridynamics. Image classification and regression studies are conducted through Convolutional Neural Networks (CNNs) and the neural processes. First, we increased the amount and quality of the data using peridynamics, which can theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, we did the case study for the PMB, LPS, and VES models that were obtained using the peridynamic theory. Case studies were performed to classify the images using CNNs and determine the PMB, LBS, and VES models' suitability. Finally, we performed the regression analysis for the images of the crack patterns with neural processes to predict the crack patterns. In the regression problem, by representing the results of the variance according to the epochs, it can be confirmed that the result of the variance is decreased by increasing the epoch numbers through the neural processes. The most critical point of this study is that the neural processes make an accurate prediction even if there are missing or insufficient training data.

Classical principal component analysis (PCA) may suffer from the sensitivity to outliers and noise. Therefore PCA based on $\ell_1$-norm and $\ell_p$-norm ($0 < p < 1$) have been studied. Among them, the ones based on $\ell_p$-norm seem to be most interesting from the robustness point of view. However, their numerical performance is not satisfactory. Note that, although T$\ell_1$-norm is similar to $\ell_p$-norm ($0 < p < 1$) in some sense, it has the stronger suppression effect to outliers and better continuity. So PCA based on T$\ell_1$-norm is proposed in this paper. Our numerical experiments have shown that its performance is superior than PCA-$\ell_p$ and $\ell_p$SPCA as well as PCA, PCA-$\ell_1$ obviously.

Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure---a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. More specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order and achieves the $n^{-1/2}$ convergence rate for parameter estimation up to polylogarithmic factors. The GSF is implemented for several univariate and multivariate mixture models in the R package GroupSortFuse. Its finite sample performance is supported by a thorough simulation study, and its application is illustrated on two real data examples.

The extra trust brought by the model interpretation has made it an indispensable part of machine learning systems. But to explain a distilled model's prediction, one may either work with the student model itself, or turn to its teacher model. This leads to a more fundamental question: if a distilled model should give a similar prediction for a similar reason as its teacher model on the same input? This question becomes even more crucial when the two models have dramatically different structure, taking GBDT2NN for example. This paper conducts an empirical study on the new approach to explaining each prediction of GBDT2NN, and how imitating the explanation can further improve the distillation process as an auxiliary learning task. Experiments on several benchmarks show that the proposed methods achieve better performance on both explanations and predictions.

Short-term traffic forecasting based on deep learning methods, especially recurrent neural networks (RNN), has received much attention in recent years. However, the potential of RNN-based models in traffic forecasting has not yet been fully exploited in terms of the predictive power of spatial-temporal data and the capability of handling missing data. In this paper, we focus on RNN-based models and attempt to reformulate the way to incorporate RNN and its variants into traffic prediction models. A stacked bidirectional and unidirectional LSTM network architecture (SBU-LSTM) is proposed to assist the design of neural network structures for traffic state forecasting. As a key component of the architecture, the bidirectional LSTM (BDLSM) is exploited to capture the forward and backward temporal dependencies in spatiotemporal data. To deal with missing values in spatial-temporal data, we also propose a data imputation mechanism in the LSTM structure (LSTM-I) by designing an imputation unit to infer missing values and assist traffic prediction. The bidirectional version of LSTM-I is incorporated in the SBU-LSTM architecture. Two real-world network-wide traffic state datasets are used to conduct experiments and published to facilitate further traffic prediction research. The prediction performance of multiple types of multi-layer LSTM or BDLSTM models is evaluated. Experimental results indicate that the proposed SBU-LSTM architecture, especially the two-layer BDLSTM network, can achieve superior performance for the network-wide traffic prediction in both accuracy and robustness. Further, comprehensive comparison results show that the proposed data imputation mechanism in the RNN-based models can achieve outstanding prediction performance when the model's input data contains different patterns of missing values.

Of recent interest in the deep learning community, generative models have proved to be powerful tools for many tasks including synthetic data generation and style transfer [1]. Geometric deep learning is a new field interested in extending such success of deep learning to non-Euclidean structured data [2]. The development of this field is timely given the recent proliferation of point cloud and mesh structured data obtained from sources such as laserscanners [3] and CAD software [4]. Particularly, mesh based convolutional autoencoders (MeshVAEs) are now a popular tool for generating surfaces [5, 6, 7, 8]. These models process a surface via geometric convolutions that respect its intrinsic geometry. With these VAEs achieving state-of-the-art performance on tasks such as reconstruction, more attention is being given towards tasks such as latent space interpretability. Geometric disentanglement, where the latent variables controlling intrinsic (properties independent of surface embedding) and extrinsic (properties dependent on surface embedding) geometry are separated [9], is an important open problem related to such interpretability. Applications include graphics, where a typical example is a disentangled latent space separating identity and pose in the case of human body generation [10, 11].

We study finite-armed stochastic bandits where the rewards of each arm might be correlated to those of other arms. We introduce a novel phased algorithm that exploits the given structure to build confidence sets over the parameters of the true bandit problem and rapidly discard all sub-optimal arms. In particular, unlike standard bandit algorithms with no structure, we show that the number of times a suboptimal arm is selected may actually be reduced thanks to the information collected by pulling other arms. Furthermore, we show that, in some structures, the regret of an anytime extension of our algorithm is uniformly bounded over time. For these constant-regret structures, we also derive a matching lower bound. Finally, we demonstrate numerically that our approach better exploits certain structures than existing methods.

We present new large-scale algorithms for fitting a multivariate convex regression function to $n$ samples in $d$ dimensions---a key problem in shape constrained nonparametric regression with widespread applications in engineering and the applied sciences. The infinite-dimensional learning task can be expressed via a convex quadratic program (QP) with $O(nd)$ decision variables and $O(n^2)$ constraints. While instances with $n$ in the lower thousands can be addressed with current algorithms within reasonable runtimes, solving larger problems (e.g., $n\approx 10^4$ or $10^5$) are computationally challenging. To this end, we present an active set type algorithm on the Lagrangian dual (of a perturbation) of the primal QP. For computational scalability, we perform approximate optimization of the reduced sub-problems; and propose a variety of randomized augmentation rules for expanding the active set. Although the dual is not strongly convex, we present a novel linear convergence rate of our algorithm on the dual. We demonstrate that our framework can solve instances of the convex regression problem with $n=10^5$ and $d=10$---a QP with 10 billion variables---within minutes; and offers significant computational gains (e.g., in terms of memory and runtime) compared to current algorithms.