Graph Representation Learning (GRL) has become essential for modern graph data mining and learning tasks. GRL aims to capture the graph's structural information and exploit it in combination with node and edge attributes to compute low-dimensional representations. While Graph Neural Networks (GNNs) have been used in state-of-the-art GRL architectures, they have been shown to suffer from over smoothing when many GNN layers need to be stacked. In a different GRL approach, spectral methods based on graph filtering have emerged addressing over smoothing; however, up to now, they employ traditional neural networks that cannot efficiently exploit the structure of graph data. Motivated by this, we propose PointSpectrum, a spectral method that incorporates a set equivariant network to account for a graph's structure. PointSpectrum enhances the efficiency and expressiveness of spectral methods, while it outperforms or competes with state-of-the-art GRL methods. Overall, PointSpectrum addresses over smoothing by employing a graph filter and captures a graph's structure through set equivariance, lying on the intersection of GNNs and spectral methods. Our findings are promising for the benefits and applicability of this architectural shift for spectral methods and GRL.

We propose a detailed analysis of the online-learning problem for Independent Cascade (IC) models under node-level feedback. These models have widespread applications in modern social networks. Existing works for IC models have only shed light on edge-level feedback models, where the agent knows the explicit outcome of every observed edge. Little is known about node-level feedback models, where only combined outcomes for sets of edges are observed; in other words, the realization of each edge is censored. This censored information, together with the nonlinear form of the aggregated influence probability, make both parameter estimation and algorithm design challenging. We establish the first confidence-region result under this setting. We also develop an online algorithm achieving a cumulative regret of $\mathcal{O}( \sqrt{T})$, matching the theoretical regret bound for IC models with edge-level feedback.

This paper considers joint analysis of multiple functionally related structures in classification tasks. In particular, our method developed is driven by how functionally correlated brain structures vary together between autism and control groups. To do so, we devised a method based on a novel combination of (1) non-Euclidean statistics that can faithfully represent non-Euclidean data in Euclidean spaces and (2) a non-parametric integrative analysis method that can decompose multi-block Euclidean data into joint, individual, and residual structures. We find that the resulting joint structure is effective, robust, and interpretable in recognizing the underlying patterns of the joint variation of multi-block non-Euclidean data. We verified the method in classifying the structural shape data collected from cases that developed and did not develop into Autistic Spectrum Disorder (ASD).

Kernel ridge regression (KRR) is a popular scheme for non-linear non-parametric learning. However, existing implementations of KRR require that all the data is stored in the main memory, which severely limits the use of KRR in contexts where data size far exceeds the memory size. Such applications are increasingly common in data mining, bioinformatics, and control. A powerful paradigm for computing on data sets that are too large for memory is the streaming model of computation, where we process one data sample at a time, discarding each sample before moving on to the next one. In this paper, we propose StreaMRAK - a streaming version of KRR. StreaMRAK improves on existing KRR schemes by dividing the problem into several levels of resolution, which allows continual refinement to the predictions. The algorithm reduces the memory requirement by continuously and efficiently integrating new samples into the training model. With a novel sub-sampling scheme, StreaMRAK reduces memory and computational complexities by creating a sketch of the original data, where the sub-sampling density is adapted to the bandwidth of the kernel and the local dimensionality of the data. We present a showcase study on two synthetic problems and the prediction of the trajectory of a double pendulum. The results show that the proposed algorithm is fast and accurate.

Word embeddings are a powerful natural lan-guage processing technique, but they are ex-tremely difficult to interpret. To enable inter-pretable NLP models, we create vectors whereeach dimension isinherently interpretable. Byinherently interpretable, we mean a systemwhere each dimension is associated with somehuman-understandablehintthat can describethe meaning of that dimension. In order tocreate more interpretable word embeddings,we transform pretrained dense word embed-dings into sparse embeddings. These new em-beddings are inherently interpretable: each oftheir dimensions is created from and repre-sents a natural language word or specific gram-matical concept. We construct these embed-dings through sparse coding, where each vec-tor in the basis set is itself a word embedding.Therefore, each dimension of our sparse vec-tors corresponds to a natural language word.We also show that models trained using thesesparse embeddings can achieve good perfor-mance and are more interpretable in practice,including through human evaluations.

In Machine Learning, an error is an important measure of how accurately our model can predict on data that it uses to learn as well as how it behaves with new and unseen data. Based on the error, we tend to choose the machine learning model which would produce the best performance on a particular dataset. In this article, we will be discussing one such problem in machine learning models known as the Bias-Variance Tradeoff. We will try to explore what it is and how one can overcome it. Below is the outline of important points that we will cover in this article.

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In Machine Learning, an error is an important measure of how accurately our model can predict on data that it uses to learn as well as how it behaves with new and unseen data. Based on the error, we tend to choose the machine learning model which would produce the best performance on a particular dataset. In this article, we will be discussing one such problem in machine learning models known as the Bias-Variance Tradeoff. We will try to explore what it is and how one can overcome it. Below is the outline of important points that we will cover in this article.

Recapping the primary step when conducting a model analysis, it is always important to import libraries and modules to access specific features. The standard imports are added, such as Matplotlib, pandas, NumPy and seaborn, as well as sklearn which allows us to split our sets into testing and training sets, along with the preprocessing of our data. On the 7th and 8th lines, we integrate TensorFlow with Keras. Keras is a high-level API of TensorFlow, so we must import them this way. The data being explored is a set consisting of patients' tumour data. Depending on the tumour size, our data will tell us if the patient is susceptible to cancer or not. Below is the data of the first 10 patients in the dataset. There are 101 patients in total.

We study the few-shot learning (FSL) problem, where a model learns to recognize new objects with extremely few labeled training data per category. Most of previous FSL approaches resort to the meta-learning paradigm, where the model accumulates inductive bias through learning many training tasks so as to solve a new unseen few-shot task. In contrast, we propose a simple approach to exploit unlabeled data accompanying the few-shot task for improving few-shot performance. Firstly, we propose a Dependency Maximization method based on the Hilbert-Schmidt norm of the cross-covariance operator, which maximizes the statistical dependency between the embedded feature of those unlabeled data and their label predictions, together with the supervised loss over the support set. We then use the obtained model to infer the pseudo-labels for those unlabeled data. Furthermore, we propose anInstance Discriminant Analysis to evaluate the credibility of each pseudo-labeled example and select the most faithful ones into an augmented support set to retrain the model as in the first step. We iterate the above process until the pseudo-labels for the unlabeled data becomes stable. Following the standard transductive and semi-supervised FSL setting, our experiments show that the proposed method out-performs previous state-of-the-art methods on four widely used benchmarks, including mini-ImageNet, tiered-ImageNet, CUB, and CIFARFS.