In this work, we first attempt to replicate an earlier study on gene selection and clustering, and then we extend this work by applying a different type of hierarchical clustering to dis- cover interesting subsets of genes from breast cancer data. Replication of such studies is a known challenge and an ac- tive area of research in bioinformatics. The work presented in this paper is three-fold. First, we replicate a study conducted at the University of North Carolina to generate an initial set of genes. Second, we apply an approach called Distance Weighted Discrimination to fuse multiple, disparate breast cancer datasets into a single validation set. Third, we per- form hierarchical clustering and k-means clustering on this validation set to discover natural groupings and compare the clusters generated by both methods. While applying the hi- erarchical clustering is part of the reproduction step, we ex- tend the research by trying two different forms of hierarchi- cal clustering. We also apply k-means clustering for the same purpose and compare all three methods using Kaplan-Meier estimation and Cox proportional hazards regression. We dis- cover that among the three methods, k-means clustering gives us the best results.

In many applications, training machine learning models involves using large amounts of human-annotated data. Obtaining precise labels for the data is expensive. Instead, training with weak supervision provides a low-cost alternative. We propose a novel weak supervision algorithm that processes noisy labels, i.e., weak signals, while also considering features of the training data to produce accurate labels for training. Our method searches over classifiers of the data representation to find plausible labelings. We call this paradigm data consistent weak supervision. A key facet of our framework is that we are able to estimate labels for data examples low or no coverage from the weak supervision. In addition, we make no assumptions about the joint distribution of the weak signals and true labels of the data. Instead, we use weak signals and the data features to solve a constrained optimization that enforces data consistency among the labels we generate. Empirical evaluation of our method on different datasets shows that it significantly outperforms state-of-the-art weak supervision methods on both text and image classification tasks.

We present a meta-method for initializing (seeding) the $k$-means clustering algorithm called PNN-smoothing. It consists in splitting a given dataset into $J$ random subsets, clustering each of them individually, and merging the resulting clusterings with the pairwise-nearest-neighbor (PNN) method. It is a meta-method in the sense that when clustering the individual subsets any seeding algorithm can be used. If the computational complexity of that seeding algorithm is linear in the size of the data $N$ and the number of clusters $k$, PNN-smoothing is also almost linear with an appropriate choice of $J$, and in fact only at most a few percent slower in most cases in practice. We show empirically, using several existing seeding methods and testing on several synthetic and real datasets, that this procedure results in systematically better costs. It can even be applied recursively, and easily parallelized. Our implementation is publicly available at https://github.com/carlobaldassi/KMeansPNNSmoothing.jl

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large (or even moderate) datasets. In this paper, we introduce a linear time complexity algorithm for approximating an SDP relaxed $K$-means clustering. The proposed sketch-and-lift (SL) approach solves an SDP on a subsampled dataset and then propagates the solution to all data points by a nearest-centroid rounding procedure. It is shown that the SL approach enjoys a similar exact recovery threshold as the $K$-means SDP on the full dataset, which is known to be information-theoretically tight under the Gaussian mixture model. The SL method can be made adaptive with enhanced theoretic properties when the cluster sizes are unbalanced. Our simulation experiments demonstrate that the statistical accuracy of the proposed method outperforms state-of-the-art fast clustering algorithms without sacrificing too much computational efficiency, and is comparable to the original $K$-means SDP with substantially reduced runtime.

BioBERT and BioMegatron are Transformers models adapted for the biomedical domain based on publicly available biomedical corpora. As such, they have the potential to encode large-scale biological knowledge. We investigate the encoding and representation of biological knowledge in these models, and its potential utility to support inference in cancer precision medicine - namely, the interpretation of the clinical significance of genomic alterations. We compare the performance of different transformer baselines; we use probing to determine the consistency of encodings for distinct entities; and we use clustering methods to compare and contrast the internal properties of the embeddings for genes, variants, drugs and diseases. We show that these models do indeed encode biological knowledge, although some of this is lost in fine-tuning for specific tasks. Finally, we analyse how the models behave with regard to biases and imbalances in the dataset.

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics Potts model. Generalizations to other multi-class problems such as community detection, data clustering, and the minimum clique cover problem are straightforward. We provide numerical benchmark results and illustrate our approach with an end-to-end application for a real-world scheduling use case within a comprehensive encode-process-decode framework. Our optimization approach performs on par or outperforms existing solvers, with the ability to scale to problems with millions of variables.

We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The algorithm is controlled by two scalar parameters, namely a distance parameter for the aggregation and another parameter controlling the minimal cluster size. Extensive experiments are conducted to give a comprehensive evaluation of the clustering performance on synthetic and real-world datasets, with various cluster shapes and low to high feature dimensionality. Our experiments demonstrate that CLASSIX competes with state-of-the-art clustering algorithms. The algorithm has linear space complexity and achieves near linear time complexity on a wide range of problems. Its inherent simplicity allows for the generation of intuitive explanations of the computed clusters.

Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g. there are highly correlated groups of variables). To improve prediction accuracy, various methods have been proposed to identify variable clusters from the data and integrate cluster information into a sparse modeling process. But none of these methods achieve satisfactory performance for prediction, variable selection and variable clustering simultaneously. This paper presents Variable Cluster Principal Component Regression (VC-PCR), a prediction method that supervises variable selection and variable clustering in order to solve this problem. Experiments with real and simulated data demonstrate that, compared to competitor methods, VC-PCR achieves better prediction, variable selection and clustering performance when cluster structure is present.

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction. Their performances are less impressive on community detection problems where, according to recent and concurring experimental evaluations, they are often outperformed by simpler alternatives such as the Louvain method. It is currently still unclear to which extent one can improve community detection with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on link prediction. In this paper, we show that jointly addressing these two tasks with high accuracy is possible. For this purpose, we introduce and theoretically study a community-preserving message passing scheme, doping our GAE and VGAE encoders by considering both the initial graph structure and modularity-based prior communities when computing embedding spaces. We also propose novel training and optimization strategies, including the introduction of a modularity-inspired regularizer complementing the existing reconstruction losses for joint link prediction and community detection. We demonstrate the empirical effectiveness of our approach, referred to as Modularity-Aware GAE and VGAE, through in-depth experimental validation on various real-world graphs.