We consider the problem of learning from training data obtained in different contexts, where the test data is subject to distributional shifts. We develop a distributionally robust method that focuses on excess risks and achieves a more appropriate trade-off between performance and robustness than the conventional and overly conservative minimax approach. The proposed method is computationally feasible and provides statistical guarantees. We demonstrate its performance using both real and synthetic data.

Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However, it is not known whether convex clustering preserves desirable properties of these algorithms. A common expectation is that convex clustering may learn difficult cluster types such as non-convex ones. Current understanding of convex clustering is limited to only consistency results on well-separated clusters. We show new understanding of its solutions. We prove that convex clustering can only learn convex clusters. We then show that the clusters have disjoint bounding balls with significant gaps. We further characterize the solutions, regularization hyperparameters, inclusterable cases and consistency.

User response prediction, which aims to predict the probability that a user will provide a predefined positive response in a given context such as clicking on an ad or purchasing an item, is crucial to many industrial applications such as online advertising, recommender systems, and search ranking. However, due to the high dimensionality and super sparsity of the data collected in these tasks, handcrafting cross features is inevitably time expensive. Prior studies in predicting user response leveraged the feature interactions by enhancing feature vectors with products of features to model second-order or high-order cross features, either explicitly or implicitly. Nevertheless, these existing methods can be hindered by not learning sufficient cross features due to model architecture limitations or modeling all high-order feature interactions with equal weights. This work aims to fill this gap by proposing a novel architecture Deep Cross Attentional Product Network (DCAP), which keeps cross network's benefits in modeling high-order feature interactions explicitly at the vector-wise level. Beyond that, it can differentiate the importance of different cross features in each network layer inspired by the multi-head attention mechanism and Product Neural Network (PNN), allowing practitioners to perform a more in-depth analysis of user behaviors. Additionally, our proposed model can be easily implemented and train in parallel. We conduct comprehensive experiments on three real-world datasets. The results have robustly demonstrated that our proposed model DCAP achieves superior prediction performance compared with the state-of-the-art models.

Link prediction on knowledge graphs (KGs) is a key research topic. Previous work mainly focused on binary relations, paying less attention to higher-arity relations although they are ubiquitous in real-world KGs. This paper considers link prediction upon n-ary relational facts and proposes a graph-based approach to this task. The key to our approach is to represent the n-ary structure of a fact as a small heterogeneous graph, and model this graph with edge-biased fully-connected attention. The fully-connected attention captures universal inter-vertex interactions, while with edge-aware attentive biases to particularly encode the graph structure and its heterogeneity. In this fashion, our approach fully models global and local dependencies in each n-ary fact, and hence can more effectively capture associations therein. Extensive evaluation verifies the effectiveness and superiority of our approach. It performs substantially and consistently better than current state-of-the-art across a variety of n-ary relational benchmarks. Our code is publicly available.

Meta-learning synthesizes and leverages the knowledge from a given set of tasks to rapidly learn new tasks using very little data. Meta-learning of linear regression tasks, where the regressors lie in a low-dimensional subspace, is an extensively-studied fundamental problem in this domain. However, existing results either guarantee highly suboptimal estimation errors, or require $\Omega(d)$ samples per task (where $d$ is the data dimensionality) thus providing little gain over separately learning each task. In this work, we study a simple alternating minimization method (MLLAM), which alternately learns the low-dimensional subspace and the regressors. We show that, for a constant subspace dimension MLLAM obtains nearly-optimal estimation error, despite requiring only $\Omega(\log d)$ samples per task. However, the number of samples required per task grows logarithmically with the number of tasks. To remedy this in the low-noise regime, we propose a novel task subset selection scheme that ensures the same strong statistical guarantee as MLLAM, even with bounded number of samples per task for arbitrarily large number of tasks.

I am actually meeting this topic in my Data Science Internship. I have already seen it during university, but I never understood really well the reasons we should use this method. Most of the times it was explained in high theoretical terms without giving examples of applications in the real world. So, what is Principal Components analysis? Why should we utilize it?

Converting raw and quantitative data into organized and informative information needs a lot of brain power and understanding. It is true that everyone can't be Aryabhatta but, you can be hardworking, focused and dedicated. So, it is time to show your dedication and hard work for learning maths and statistics for data science. Mathematics and Statistics are two of the most important concepts of Data Science. Data Science revolves around these two fields and draws their concepts to operate on the data. Today, we will explore the various concepts that build up data science and their practical usages in this field.

This article will answer these questions. Apart from all this, we will also learn more about K-means clustering and its implementation by defining K-means fit function. Clustering is an unsupervised learning technique. It is used to group different data points based on similar features or characteristics. For example, A company wants to know to whom they should display a particular ad such the chances of clicking it increases. Now suppose you have all the user's clusters with the ads each group mostly clicks.

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