Typically, hashing methods are essential for the use of Jaccard similarity tobepractical inlarge-scale settings.

Neural Information Processing Systems http://nips.cc/

Z that represents some transfer of mass between elements of w and v . The proof is the same for W . Proposition 2. Suppose that the target row and column representative distributions are the same, The the Kantorovich OT problem and whose rank is at most min(rank(Z), rank( W)) . Proof of proposition 2. From linear algebra, we have that Proof of proposition 3. We suppose that The optimal transport problem can be formulated and solved as the Earth Mover's Distance (EMD) We report the biclustering performance on the synthetic datasets in table 2. At least one of our models finds the perfect partition in all cases. The gene-expression matrices used are the Cumida Breast Cancer and Leukemia datasets. Their characteristics are shown in Table 3. Table 3: Characteristics of the gene expression datasets.

Coreset is a small set that provides a data summary for a large dataset, such that training solely on the small set achieves competitive performance compared with a large dataset. In rehearsal-based continual learning, the coreset is typically used in the memory replay buffer to stand for representative samples in previous tasks, and the coreset selection procedure is typically formulated as a bilevel problem. However, the typical bilevel formulation for coreset selection explicitly performs optimization over discrete decision variables with greedy search, which is computationally expensive. Several works consider other formulations to address this issue, but they ignore the nested nature of bilevel optimization problems and may not solve the bilevel coreset selection problem accurately. To address these issues, we propose a new bilevel formulation, where the inner problem tries to find a model which minimizes the expected training error sampled from a given probability distribution, and the outer problem aims to learn the probability distribution with approximately $K$ (coreset size) nonzero entries such that learned model in the inner problem minimizes the training error over the whole data. To ensure the learned probability has approximately $K$ nonzero entries, we introduce a novel regularizer based on the smoothed top-$K$ loss in the upper problem.

In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network. We propose a novel graphical model, namely Latent Differential Graph Model, where the networks under two different conditions are represented by two semiparametric elliptical distributions respectively, and the variation of these two networks ( i.e.,

Neural Information Processing Systems http://nips.cc/

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our analysis demonstrates that, by fixing the support set, the global solution of the minimization subproblem for the proximal linearization of the objective function can be computed in closed form with at most $n$ nonzero entries. Exploiting this structural property offers a powerful avenue for dramatically enhancing computational efficiency. Guided by this insight, we propose a support-set algorithm preserving strictly the feasibility of iterates. A central ingredient is a strategically devised update scheme for support sets that adjusts the placement of nonzero entries. We establish the global convergence of the support-set algorithm to a first-order stationary point, and show that its iteration complexity required to reach an $ε$-approximate first-order stationary point is $O (ε^{-2})$. Numerical results are strongly in favor of our algorithm in real-world applications, including nonnegative PCA, clustering, and community detection.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/