The edge partition model (EPM) is a fundamental Bayesian nonparametric model for extracting an overlapping structure from binary matrix. The EPM adopts a gamma process ($\Gamma$P) prior to automatically shrink the number of active atoms. However, we empirically found that the model shrinkage of the EPM does not typically work appropriately and leads to an overfitted solution. An analysis of the expectation of the EPM's intensity function suggested that the gamma priors for the EPM hyperparameters disturb the model shrinkage effect of the internal $\Gamma$P. In order to ensure that the model shrinkage effect of the EPM works in an appropriate manner, we proposed two novel generative constructions of the EPM: CEPM incorporating constrained gamma priors, and DEPM incorporating Dirichlet priors instead of the gamma priors. Furthermore, all DEPM's model parameters including the infinite atoms of the $\Gamma$P prior could be marginalized out, and thus it was possible to derive a truly infinite DEPM (IDEPM) that can be efficiently inferred using a collapsed Gibbs sampler. We experimentally confirmed that the model shrinkage of the proposed models works well and that the IDEPM indicated state-of-the-art performance in generalization ability, link prediction accuracy, mixing efficiency, and convergence speed.

Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such `shift-invariant' atoms. Even though some success has been reported with existing algorithms, they are limited in applicability due to their heuristic nature. Moreover, they are often vulnerable to artifacts and impulsive noise, which are typically present in raw neural recordings. In this study, we address these issues and propose a novel probabilistic convolutional sparse coding (CSC) model for learning shift-invariant atoms from raw neural signals containing potentially severe artifacts.

Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear (O(1/t)) convergence on general smooth and convex objectives, and linear convergence (O(e^{-t})) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.

Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We present an alternative notion of exchangeability for random graphs, which we call edge exchangeability, in which the distribution of a graph sequence is invariant to the order of the edges. We demonstrate that edge-exchangeable models, unlike models that are traditionally vertex exchangeable, can exhibit sparsity. To do so, we outline a general framework for graph generative models; by contrast to the pioneering work of Caron and Fox (2015), models within our framework are stationary across steps of the graph sequence. In particular, our model grows the graph by instantiating more latent atoms of a single random measure as the dataset size increases, rather than adding new atoms to the measure.

We propose a multivariate online dictionary-learning method for obtaining decompositions of brain images with structured and sparse components (aka atoms). Sparsity is to be understood in the usual sense: the dictionary atoms are constrained to contain mostly zeros. This is imposed via an $\ell_1$-norm constraint. By structured, we mean that the atoms are piece-wise smooth and compact, thus making up blobs, as opposed to scattered patterns of activation. We propose to use a Sobolev (Laplacian) penalty to impose this type of structure. Combining the two penalties, we obtain decompositions that properly delineate brain structures from functional images. This non-trivially extends the online dictionary-learning work of Mairal et al. (2010), at the price of only a factor of 2 or 3 on the overall running time. Just like the Mairal et al. (2010) reference method, the online nature of our proposed algorithm allows it to scale to arbitrarily sized datasets. Experiments on brain data show that our proposed method extracts structured and denoised dictionaries that are more intepretable and better capture inter-subject variability in small medium, and large-scale regimes alike, compared to state-of-the-art models.

We consider the problem of crystal materials generation using language models (LMs).

However, some critical aspects of it, such as the relationship between superconductivity and materials' chemical/structural features, still need to be understood. Recent successes of data-driven approaches in material science strongly inspire researchers to study this relationship with them, but a corresponding dataset is still lacking.