The existing methods to calculate the Eigenvector Centrality(EC) tend to not be robust enough for determination of EC in low time complexity or not well-scalable for large networks, hence rendering them practically unreliable/ computationally expensive. So, it is of the essence to develop a method that is scalable in low computational time. Hence, we propose a deep learning model for the identification of nodes with high Eigenvector Centrality. There have been a few previous works in identifying the high ranked nodes with supervised learning methods, but in real-world cases, the graphs are not labelled and hence deployment of supervised learning methods becomes a hazard and its usage becomes impractical. So, we devise CUL(Centrality with Unsupervised Learning) method to learn the relative EC scores in a network in an unsupervised manner. To achieve this, we develop an Encoder-Decoder based framework that maps the nodes to their respective estimated EC scores. Extensive experiments were conducted on different synthetic and real-world networks. We compared CUL against a baseline supervised method for EC estimation similar to some of the past works. It was observed that even with training on a minuscule number of training datasets, CUL delivers a relatively better accuracy score when identifying the higher ranked nodes than its supervised counterpart. We also show that CUL is much faster and has a smaller runtime than the conventional baseline method for EC computation. The code is available at https://github.com/codexhammer/CUL.

Data on high-dimensional spheres arise frequently in many disciplines either naturally or as a consequence of preliminary processing and can have intricate dependence structure that needs to be understood. We develop exploratory factor analysis of the projected normal distribution to explain the variability in such data using a few easily interpreted latent factors. Our methodology provides maximum likelihood estimates through a novel fast alternating expectation profile conditional maximization algorithm. Results on simulation experiments on a wide range of settings are uniformly excellent. Our methodology provides interpretable and insightful results when applied to tweets with the $\#MeToo$ hashtag in early December 2018, to time-course functional Magnetic Resonance Images of the average pre-teen brain at rest, to characterize handwritten digits, and to gene expression data from cancerous cells in the Cancer Genome Atlas.

Bayesian optimization is a popular optimization technique for optimizing a black box function especially with high dimensions. For a known objective functions, various optimization functions are readily available to choose from. For a black box function, since the true nature of the objective function is unknown, many available optimization techniques including Gradient Descent cannot be applied. For a black box function, various other optimization techniques are available such as Grid Search and Random Search, however, both of these techniques are extremely inefficient and time consuming specially if the objective function is costly to execute. Instead, Bayesian optimization tries to find the global optimum by using a surrogate function to evaluate the real objective function, thus, making the computation much efficient with respect to time or money.

We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic algorithms \emph{cannot} be minimax-optimal in the realizable setting. Hence, we design novel computationally efficient algorithms for the realizable setting that match the minimax lower bound up to logarithmic factors and are general-purpose, accommodating a wide variety of function classes including kernel methods, H{\"o}lder smooth functions, and convex functions. The sample complexities of our algorithms can be quantified in terms of well-known quantities like the extended teaching dimension and haystack dimension. However, unlike algorithms based directly on those combinatorial quantities, our algorithms are computationally efficient. To achieve computational efficiency, our algorithms sample from the version space using Monte Carlo "hit-and-run" algorithms instead of maintaining the version space explicitly. Our approach has two key strengths. First, it is simple, consisting of two unifying, greedy algorithms. Second, our algorithms have the capability to seamlessly leverage prior knowledge that is often available and useful in practice. In addition to our new theoretical results, we demonstrate empirically that our algorithms are competitive with Gaussian process UCB methods.

Hyperparameter optimization is a ubiquitous challenge in machine learning, and the performance of a trained model depends crucially upon their effective selection. While a rich set of tools exist for this purpose, there are currently no practical hyperparameter selection methods under the constraint of differential privacy (DP). We study honest hyperparameter selection for differentially private machine learning, in which the process of hyperparameter tuning is accounted for in the overall privacy budget. To this end, we i) show that standard composition tools outperform more advanced techniques in many settings, ii) empirically and theoretically demonstrate an intrinsic connection between the learning rate and clipping norm hyperparameters, iii) show that adaptive optimizers like DPAdam enjoy a significant advantage in the process of honest hyperparameter tuning, and iv) draw upon novel limiting behaviour of Adam in the DP setting to design a new and more efficient optimizer.

We study active sampling algorithms for linear regression, which aim to query only a small number of entries of a target vector $b\in\mathbb{R}^n$ and output a near minimizer to $\min_{x\in\mathbb{R}^d}\|Ax-b\|$, where $A\in\mathbb{R}^{n \times d}$ is a design matrix and $\|\cdot\|$ is some loss function. For $\ell_p$ norm regression for any $0

In this paper we propose an active metric learning method for clustering with pairwise constraints. The proposed method actively queries the label of informative instance pairs, while estimating underlying metrics by incorporating unlabeled instance pairs, which leads to a more accurate and efficient clustering process. In particular, we augment the queried constraints by generating more pairwise labels to provide additional information in learning a metric to enhance clustering performance. Furthermore, we increase the robustness of metric learning by updating the learned metric sequentially and penalizing the irrelevant features adaptively. In addition, we propose a novel active query strategy that evaluates the information gain of instance pairs more accurately by incorporating the neighborhood structure, which improves clustering efficiency without extra labeling cost. In theory, we provide a tighter error bound of the proposed metric learning method utilizing augmented queries compared with methods using existing constraints only. Furthermore, we also investigate the improvement using the active query strategy instead of random selection. Numerical studies on simulation settings and real datasets indicate that the proposed method is especially advantageous when the signal-to-noise ratio between significant features and irrelevant features is low.

Model selection in contextual bandits is an important complementary problem to regret minimization with respect to a fixed model class. We consider the simplest non-trivial instance of model-selection: distinguishing a simple multi-armed bandit problem from a linear contextual bandit problem. Even in this instance, current state-of-the-art methods explore in a suboptimal manner and require strong "feature-diversity" conditions. In this paper, we introduce new algorithms that a) explore in a data-adaptive manner, and b) provide model selection guarantees of the form $\mathcal{O}(d^{\alpha} T^{1- \alpha})$ with no feature diversity conditions whatsoever, where $d$ denotes the dimension of the linear model and $T$ denotes the total number of rounds. The first algorithm enjoys a "best-of-both-worlds" property, recovering two prior results that hold under distinct distributional assumptions, simultaneously. The second removes distributional assumptions altogether, expanding the scope for tractable model selection. Our approach extends to model selection among nested linear contextual bandits under some additional assumptions.

A widely used algorithm for transfer learning is fine-tuning, where a pre-trained model is fine-tuned on a target task with a small amount of labeled data. When the capacity of the pre-trained model is much larger than the size of the target data set, fine-tuning is prone to overfitting and "memorizing" the training labels. Hence, an important question is to regularize fine-tuning and ensure its robustness to noise. To address this question, we begin by analyzing the generalization properties of fine-tuning. We present a PAC-Bayes generalization bound that depends on the distance traveled in each layer during fine-tuning and the noise stability of the fine-tuned model. We empirically measure these quantities. Based on the analysis, we propose regularized self-labeling -- the interpolation between regularization and self-labeling methods, including (i) layer-wise regularization to constrain the distance traveled in each layer; (ii) self label-correction and label-reweighting to correct mislabeled data points (that the model is confident) and reweight less confident data points. We validate our approach on an extensive collection of image and text data sets using multiple pre-trained model architectures. Our approach improves baseline methods by 1.76% (on average) for seven image classification tasks and 0.75% for a few-shot classification task. When the target data set includes noisy labels, our approach outperforms baseline methods by 3.56% on average in two noisy settings.

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of `automatic relevance determination' kernels, but in high-dimensional datasets this approach can be unreliable. A more probabilistically principled alternative is to use spike and slab priors and infer a posterior probability of variable inclusion. However, existing implementations in GPs are extremely costly to run in both high-dimensional and large-$n$ datasets, or are intractable for most kernels. As such, we develop a fast and scalable variational inference algorithm for the spike and slab GP that is tractable with arbitrary differentiable kernels. We improve our algorithm's ability to adapt to the sparsity of relevant variables by Bayesian model averaging over hyperparameters, and achieve substantial speed ups using zero temperature posterior restrictions, dropout pruning and nearest neighbour minibatching. In experiments our method consistently outperforms vanilla and sparse variational GPs whilst retaining similar runtimes (even when $n=10^6$) and performs competitively with a spike and slab GP using MCMC but runs up to $1000$ times faster.