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Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as cliques for various reasons, e.g., data noise. Therefore, $k$-plex, -- graph with each vertex adjacent to all but at most $k$ vertices, is introduced as a relaxed version of clique. Often, to better simulate cohesive communities, an emphasis is placed on connected $k$-plexes with small $k$. In this paper, we continue the research line of listing all maximal $k$-plexes and maximal $k$-plexes of prescribed size. Our first contribution is algorithm \emph{ListPlex} that lists all maximal $k$-plexes in $O^*(\gamma^D)$ time for each constant $k$, where $\gamma$ is a value related to $k$ but strictly smaller than 2, and $D$ is the degeneracy of the graph that is far less than the vertex number $n$ in real-word graphs. Compared to the trivial bound of $2^n$, the improvement is significant, and our bound is better than all previously known results. In practice, we further use several techniques to accelerate listing $k$-plexes of a given size, such as structural-based prune rules, cache-efficient data structures, and parallel techniques. All these together result in a very practical algorithm. Empirical results show that our approach outperforms the state-of-the-art solutions by up to orders of magnitude.

Machine learning-based data-driven modeling can allow computationally efficient time-dependent solutions of PDEs, such as those that describe subsurface multiphysical problems. In this work, our previous approach of conditional generative adversarial networks (cGAN) developed for the solution of steady-state problems involving highly heterogeneous material properties is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. We note that this approach can accommodate other continuous variables (e.g., Young's modulus) similar to the time domain, which makes this framework highly flexible and extendable. Moreover, this framework can handle training data that contain different timestamps and then predict timestamps that do not exist in the training data. As a numerical example, the transient response of the coupled poroelastic process is studied in two different permeability fields: Zinn \& Harvey transformation and a bimodal transformation. The proposed CcGAN uses heterogeneous permeability fields as input parameters while pressure and displacement fields over time are model output. Our results show that the model provides sufficient accuracy with computational speed-up. This robust framework will enable us to perform real-time reservoir management and robust uncertainty quantification in realistic problems.

We propose a new simulation-based estimation method, adversarial estimation, for structural models. The estimator is formulated as the solution to a minimax problem between a generator (which generates synthetic observations using the structural model) and a discriminator (which classifies if an observation is synthetic). The discriminator maximizes the accuracy of its classification while the generator minimizes it. We show that, with a sufficiently rich discriminator, the adversarial estimator attains parametric efficiency under correct specification and the parametric rate under misspecification. We advocate the use of a neural network as a discriminator that can exploit adaptivity properties and attain fast rates of convergence. We apply our method to the elderly's saving decision model and show that our estimator uncovers the bequest motive as an important source of saving across the wealth distribution, not only for the rich.

Empirical risk minimization (ERM) is known in practice to be non-robust to distributional shift where the training and the test distributions are different. A suite of approaches, such as importance weighting, and variants of distributionally robust optimization (DRO), have been proposed to solve this problem. But a line of recent work has empirically shown that these approaches do not significantly improve over ERM in real applications with distribution shift. The goal of this work is to obtain a comprehensive theoretical understanding of this intriguing phenomenon. We first posit the class of Generalized Reweighting (GRW) algorithms, as a broad category of approaches that iteratively update model parameters based on iterative reweighting of the training samples. We show that when overparameterized models are trained under GRW, the resulting models are close to that obtained by ERM. We also show that adding small regularization which does not greatly affect the empirical training accuracy does not help. Together, our results show that a broad category of what we term GRW approaches are not able to achieve distributionally robust generalization. Our work thus has the following sobering takeaway: to make progress towards distributionally robust generalization, we either have to develop non-GRW approaches, or perhaps devise novel classification/regression loss functions that are adapted to the class of GRW approaches.

Generative adversarial networks (GANs) with clustered latent spaces can perform conditional generation in a completely unsupervised manner. In the real world, the salient attributes of unlabeled data can be imbalanced. However, most of existing unsupervised conditional GANs cannot cluster attributes of these data in their latent spaces properly because they assume uniform distributions of the attributes. To address this problem, we theoretically derive Stein latent optimization that provides reparameterizable gradient estimations of the latent distribution parameters assuming a Gaussian mixture prior in a continuous latent space. Structurally, we introduce an encoder network and novel unsupervised conditional contrastive loss to ensure that data generated from a single mixture component represent a single attribute. We confirm that the proposed method, named Stein Latent Optimization for GANs (SLOGAN), successfully learns balanced or imbalanced attributes and achieves state-of-the-art unsupervised conditional generation performance even in the absence of attribute information (e.g., the imbalance ratio). Moreover, we demonstrate that the attributes to be learned can be manipulated using a small amount of probe data.

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.

When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the variability of the estimate can be high in some cases. An important result by Bengio and Grandvalet (2004) states that no general unbiased variance estimator can be constructed, that would apply for any utility or loss measure and any model. We show that it is possible to construct an unbiased estimator considering a specific predictive performance measure and model. We demonstrate an unbiased sampling distribution variance estimator for the Bayesian normal model with fixed model variance using the expected log pointwise predictive density (elpd) utility score. This example demonstrates that it is possible to obtain improved, problem-specific, unbiased estimators for assessing the uncertainty in LOO-CV estimation.

Spatio-temporal models are widely used in many research areas from ecology to epidemiology. However, most covariance functions describe spatial relationships based on Euclidean distance only. In this paper, we introduce the R package SSNbayes for fitting Bayesian spatio-temporal models and making predictions on branching stream networks. SSNbayes provides a linear regression framework with multiple options for incorporating spatial and temporal autocorrelation. Spatial dependence is captured using stream distance and flow connectivity while temporal autocorrelation is modelled using vector autoregression approaches. SSNbayes provides the functionality to make predictions across the whole network, compute exceedance probabilities and other probabilistic estimates such as the proportion of suitable habitat. We illustrate the functionality of the package using a stream temperature dataset collected in Idaho, USA.

Deep generative modelling is a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which making trade-offs including run-time, diversity, and architectural restrictions. In particular, this compendium covers energy-based models, variational autoencoders, generative adversarial networks, autoregressive models, normalizing flows, in addition to numerous hybrid approaches. These techniques are drawn under a single cohesive framework, comparing and contrasting to explain the premises behind each, while reviewing current state-of-the-art advances and implementations.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.