Dense retrievers bridge vocabulary gaps but suffer from semantic drift, ranking topically similar passages that are not actually relevant to the query. Sparse retrievers like BM25 are generally less prone to such false positives but miss paraphrases. We observe that these failure modes are complementary, with relevant passages concentrated in regions where both retrievers score highly, while single-retriever confidence proves unreliable. Building on this insight, we propose AgreRank, a re-ranking method that leverages sparse-dense consensus for query expansion. AgreRank identifies anchor documents where both retrievers agree, expands the query through these verified anchors, and applies geometric gating to suppress drift from the original intent. On TREC Deep Learning 2021 and 2022, AgreRank improves over Dense+CE by 3.4--5.7% and over RRF+CE by 3.7--5.6% under identical retrieval and reranking components, achieving nDCG@10 of 0.706 and 0.627 with a lightweight 33M-parameter cross-encoder. These gains require no additional parameters or training, demonstrating that more effective use of retrieval signals offers a practical alternative to model scaling.

Graph neural networks (GNNs) have emerged as a powerful framework for a wide range of node-level graph learning tasks. However, their performance typically depends on random or minimally informed initial feature representations, where poor initialization can lead to slower convergence and increased training instability. In this paper, we address this limitation by leveraging a statistically grounded one-hot graph encoder embedding (GEE) as a high-quality, structure-aware initialization for node features. Integrating GEE into standard GNNs yields the GEE-powered GNN (GG) framework. Across extensive simulations and real-world benchmarks, GG provides consistent and substantial performance gains in both unsupervised and supervised settings. For node classification, we further introduce GG-C, which concatenates the outputs of GG and GEE and outperforms competing methods, achieving roughly 10-50% accuracy improvements across most datasets. These results demonstrate the importance of principled, structure-aware initialization for improving the efficiency, stability, and overall performance of graph neural network architecture, enabling models to better exploit graph topology from the outset.

In this article we propose a lightning fast graph embedding method called one-hot graph encoder embedding. It has a linear computational complexity and the capacity to process billions of edges within minutes on standard PC - making it an ideal candidate for huge graph processing. It is applicable to either adjacency matrix or graph Laplacian, and can be viewed as a transformation of the spectral embedding. Under random graph models, the graph encoder embedding is approximately normally distributed per vertex, and asymptotically converges to its mean. We showcase three applications: vertex classification, vertex clustering, and graph bootstrap. In every case, the graph encoder embedding exhibits unrivalled computational advantages.

Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations.

Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many recent extensions to decision forests are based on axis-oblique splits. Unfortunately, these extensions forfeit one or more of the favorable properties of decision forests based on axis-aligned splits, such as robustness to many noise dimensions, interpretability, or computational efficiency. We introduce yet another decision forest, called “Sparse Projection Oblique Randomer Forests” (SPORF). SPORF trees recursively split along very sparse random projections. Our method significantly improves accuracy over existing state-of-the-art algorithms on a standard benchmark suite for classification with $>100$ problems of varying dimension, sample size, and number of classes. To illustrate how SPORF addresses the limitations of both axis-aligned and existing oblique decision forest methods, we conduct extensive simulated experiments. SPORF typically yields improved performance over existing decision forest methods, while mitigating computational efficiency and scalability and maintaining interpretability. Very sparse random projections can be incorporated into gradient boosted trees to obtain potentially similar gains.

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of ℓ1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency under a latent subspace model and contamination. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance and significantly faster.

For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, we propose a sparse representation vertex classifier which does not require information about the model dimension. This classifier represents a test vertex as a sparse combination of the vertices in the training set and uses the recovered coefficients to classify the test vertex. We prove consistency of our proposed classifier for stochastic blockmodels, and demonstrate that the sparse representation classifier can predict vertex labels with higher accuracy than adjacency spectral embedding approaches via both simulation studies and real data experiments. Our results demonstrate the robustness and effectiveness of our proposed vertex classifier when the model dimension is unknown.