Vertex nomination is a lightly-supervised network information retrieval (IR) task in which vertices of interest in one graph are used to query a second graph to discover vertices of interest in the second graph. Similar to other IR tasks, the output of a vertex nomination scheme is a ranked list of the vertices in the second graph, with the heretofore unknown vertices of interest ideally concentrating at the top of the list. Vertex nomination schemes provide a useful suite of tools for efficiently mining complex networks for pertinent information. In this paper, we explore, both theoretically and practically, the dual roles of content (i.e., edge and vertex attributes) and context (i.e., network topology) in vertex nomination. We provide necessary and sufficient conditions under which vertex nomination schemes that leverage both content and context outperform schemes that leverage only content or context separately. While the joint utility of both content and context has been demonstrated empirically in the literature, the framework presented in this paper provides a novel theoretical basis for understanding the potential complementary roles of network features and topology.

Machine learning models trained with purely observational data and the principle of empirical risk minimization (Vapnik, 1992) can fail to generalize to unseen domains. In this paper, we focus on the case where the problem arises through spurious correlation between the observed domains and the actual task labels. We find that many domain generalization methods do not explicitly take this spurious correlation into account. Instead, especially in more application-oriented research areas like medical imaging or robotics, data augmentation techniques that are based on heuristics are used to learn domain invariant features. To bridge the gap between theory and practice, we develop a causal perspective on the problem of domain generalization. We argue that causal concepts can be used to explain the success of data augmentation by describing how they can weaken the spurious correlation between the observed domains and the task labels. We demonstrate that data augmentation can serve as a tool for simulating interventional data. Lastly, but unsurprisingly, we show that augmenting data improperly can cause a significant decrease in performance.

This paper considers the problem of neural decoding from parallel neural measurements systems such as micro-electrocorticography ($\mu$-ECoG). In systems with large numbers of array elements at very high sampling rates, the dimension of the raw measurement data may be large. Learning neural decoders for this high-dimensional data can be challenging, particularly when the number of training samples is limited. To address this challenge, this work presents a novel neural network decoder with a low-rank structure in the first hidden layer. The low-rank constraints dramatically reduce the number of parameters in the decoder while still enabling a rich class of nonlinear decoder maps. The low-rank decoder is illustrated on $\mu$-ECoG data from the primary auditory cortex (A1) of awake rats. This decoding problem is particularly challenging due to the complexity of neural responses in the auditory cortex and the presence of confounding signals in awake animals. It is shown that the proposed low-rank decoder significantly outperforms models using standard dimensionality reduction techniques such as principal component analysis (PCA).

We propose a new concept of rateless auto-encoders (RL-AEs) that enable a flexible latent dimensionality, which can be seamlessly adjusted for varying distortion and dimensionality requirements. In the proposed RL-AEs, instead of a deterministic bottleneck architecture, we use an over-complete representation that is stochastically regularized with weighted dropouts, in a manner analogous to sparse AE (SAE). Unlike SAEs, our RL-AEs employ monotonically increasing dropout rates across the latent representation nodes such that the latent variables become sorted by importance like in principal component analysis (PCA). This is motivated by the rateless property of conventional PCA, where the least important principal components can be discarded to realize variable rate dimensionality reduction that gracefully degrades the distortion. In contrast, since the latent variables of conventional AEs are equally important for data reconstruction, they cannot be simply discarded to further reduce the dimensionality after the AE model is trained. Our proposed stochastic bottleneck framework enables seamless rate adaptation with high reconstruction performance, without requiring predetermined latent dimensionality at training. We experimentally demonstrate that the proposed RL-AEs can achieve variable dimensionality reduction while achieving low distortion compared to conventional AEs.

Principal Component Analysis (PCA) is a fundamental technology in machine learning. Nowadays many high-dimension large datasets are acquired in a distributed manner, which precludes the use of centralized PCA due to the high communication cost and privacy risk. Thus, many distributed PCA algorithms are proposed, most of which, however, focus on linear cases. To efficiently extract non-linear features, this brief proposes a communication-efficient distributed kernel PCA algorithm, where linear and RBF kernels are applied. The key is to estimate the global empirical kernel matrix from the eigenvectors of local kernel matrices. The approximate error of the estimators is theoretically analyzed for both linear and RBF kernels. The result suggests that when eigenvalues decay fast, which is common for RBF kernels, the proposed algorithm gives high quality results with low communication cost. Results of simulation experiments verify our theory analysis and experiments on GSE2187 dataset show the effectiveness of the proposed algorithm.

I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes may vary in a given set. When this set is permutation symmetric, the optimal design is complete randomization, and using a single partition (i.e., the design that only randomizes the treatment labels for each side of the partition) has minimax risk larger by a factor of n 1. More generally, the optimal design is shown to be the mixed-strategy optimal design (MSOD) of Kallus (2018). Notably, even when the set of conditional mean outcomes has structure (i.e., is not permutation symmetric), being minimax-optimal for variance still requires randomization beyond a single partition. Nonetheless, since this targets precision, it may still not ensure sufficient uniformity in randomization to enable randomization (i.e., design-based) inference by Fisher's exact test to appropriately detect violations of null. I therefore propose the inferenceconstrained MSOD, which is minimax-optimal among all designs subject to such uniformity constraints. On the way, I discuss Johansson et al. (2020) who recently compared rerandomization of Morgan and Rubin (2012) and the pure-strategy optimal design (PSOD) of Kallus (2018). I point out some errors therein and set straight that randomization is minimax-optimal and that the "no free lunch" theorem and example in Kallus (2018) are correct. Keywords: Causal inference, controlled experiments, covariate balance, minimax, optimization.

Estimating the Individual Treatment Effect from observational data, defined as the difference between outcomes with and without treatment or intervention, while observing just one of both, is a challenging problems in causal learning. In this paper, we formulate this problem as an inference from hidden variables and enforce causal constraints based on a model of four exclusive causal populations. We propose a new version of the EM algorithm, coined as Expected-Causality-Maximization (ECM) algorithm and provide hints on its convergence under mild conditions. We compare our algorithm to baseline methods on synthetic and real-world data and discuss its performances.

Reproducing kernel Hilbert spaces (RKHSs) are key spaces for machine learning that are becoming popular also for linear system identification. In particular, the so-called stable RKHSs can be used to model absolutely summable impulse responses. In combination e.g. with regularized least squares they can then be used to reconstruct dynamic systems from input-output data. In this paper we provide new structural properties of stable RKHSs. The relation between stable kernels and other fundamental classes, like those containing absolutely summable or finite-trace kernels, is elucidated. These insights are then brought into the feature space context. First, it is proved that any stable kernel admits feature maps induced by a basis of orthogonal eigenvectors in l2. The exact connection with classical system identification approaches that exploit such kind of functions to model impulse responses is also provided. Then, the necessary and sufficient stability condition for RKHSs designed by formulating kernel eigenvectors and eigenvalues is obtained. Overall, our new results provide novel mathematical foundations of stable RKHSs with impact on stability tests, impulse responses modeling and computational efficiency of regularized schemes for linear system identification.

Linear mixed modelling is a popular approach for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known, estimating simultaneously the contribution of known and latent variance components in linear mixed models is a challenge that has so far relied on numerical gradient-based optimizers to maximize the likelihood function. This is unsatisfactory because the resulting solution is poorly characterized and the efficiency of the method may be suboptimal. Here we prove analytically that maximum-likelihood latent variables can always be chosen orthogonal to the known confounding factors, in other words, that maximum-likelihood latent variables explain sample covariances not already explained by known factors. Based on this result we propose a restricted maximum-likelihood method which estimates the latent variables by maximizing the likelihood on the restricted subspace orthogonal to the known confounding factors, and show that this reduces to probabilistic PCA on that subspace. The method then estimates the variance-covariance parameters by maximizing the remaining terms in the likelihood function given the latent variables, using a newly derived analytic solution for this problem. Compared to gradient-based optimizers, our method attains equal or higher likelihood values, can be computed using standard matrix operations, results in latent factors that don't overlap with any known factors, and has a runtime reduced by several orders of magnitude. We anticipate that the restricted maximum-likelihood method will facilitate the application of linear mixed modelling strategies for learning latent variance components to much larger gene expression datasets than currently possible.

Early classification of time series has been extensively studied for minimizing class prediction delay in time-sensitive applications such as healthcare and finance. A primary task of an early classification approach is to classify an incomplete time series as soon as possible with some desired level of accuracy. Recent years have witnessed several approaches for early classification of time series. As most of the approaches have solved the early classification problem with different aspects, it becomes very important to make a thorough review of the existing solutions to know the current status of the area. These solutions have demonstrated reasonable performance in a wide range of applications including human activity recognition, gene expression based health diagnostic, industrial monitoring, and so on. In this paper, we present a systematic review of current literature on early classification approaches for both univariate and multivariate time series. We divide various existing approaches into four exclusive categories based on their proposed solution strategies. The four categories include prefix based, shapelet based, model based, and miscellaneous approaches. The authors also discuss the applications of early classification in many areas including industrial monitoring, intelligent transportation, and medical. Finally, we provide a quick summary of the current literature with future research directions.