The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to construct a hierarchical tree of communities instead. This can be done with a simple top-down recursive bi-partitioning algorithm, starting with a single community and separating the nodes into two communities by spectral clustering repeatedly, until a stopping rule suggests there are no further communities. Such an algorithm is model-free, extremely fast, and requires no tuning other than selecting a stopping rule. We show that there are regimes where it outperforms $K$-way spectral clustering, and propose a natural model for analyzing the algorithm's theoretical performance, the binary tree stochastic block model. Under this model, we prove that the algorithm correctly recovers the entire community tree under relatively mild assumptions. We also apply the algorithm to a dataset of statistics papers to construct a hierarchical tree of statistical research communities.

Single-image super-resolution (SISR) is a canonical problem with diverse applications. Leading methods like SRGAN (Ledig et al., 2017) produce images that contain various artifacts, such as high-frequency noise, hallucinated colours and shape distortions, which adversely affect the realism of the result. In this paper, we propose an alternative approach based on an extension of the method of Implicit Maximum Likelihood Estimation (IMLE) (Li & Malik, 2018). We demonstrate greater effectiveness at noise reduction and preservation of the original colours and shapes, yielding more realistic super-resolved images. The problem of single-image super-resolution (SISR) aims to output a plausible high-resolution image that is consistent with a given low-resolution image. The key challenge arises from the fact that the problem is ill-posed - given the same low-resolution image, there are many different highresolution images that would be the same as the low-resolution image upon downsampling.

Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in memory, and propose more compact representations of parameter values that can be used during inference. We focus on a class of graphical models that we refer to as latent Dirichlet-Categorical models, and show how a combination of two sketching algorithms known as count-min sketch and approximate counters provide an efficient representation for them. We show that this sketch combination -- which, despite having been used before in NLP applications, has not been previously analyzed -- enjoys desirable properties. We prove that for this class of models, when the sketches are used during Markov Chain Monte Carlo inference, the equilibrium of sketched MCMC converges to that of the exact chain as sketch parameters are tuned to reduce the error rate.

Thisabstract extends on the previous work [21, 22] on program induction[16] using probabilistic programming. It describes possible further steps to extend that work, such that, ultimately, automatic probabilistic program synthesis can generalise over any reasonable set of inputs and outputs, in particular in regard to text, image and video data.

We design and analyze TS-Cascade, a Thompson sampling algorithm for the cascading bandit problem. In TS-Cascade, Bayesian estimates of the click probability are constructed using a univariate Gaussian; this leads to a more efficient exploration procedure vis-\`a-vis existing UCB-based approaches. We also incorporate the empirical variance of each item's click probability into the Bayesian updates. These two novel features allow us to prove an expected regret bound of the form $\tilde{O}(\sqrt{KLT})$ where $L$ and $K$ are the number of ground items and the number of items in the chosen list respectively and $T\ge L$ is the number of Thompson sampling update steps. This matches the state-of-the-art regret bounds for UCB-based algorithms. More importantly, it is the first theoretical guarantee on a Thompson sampling algorithm for any stochastic combinatorial bandit problem model with partial feedback. Empirical experiments demonstrate superiority of TS-Cascade compared to existing UCB-based procedures in terms of the expected cumulative regret and the time complexity.

In this article, we investigate the features which enhanced discriminate the survival in the micro and small business (MSE) using the approach of data mining with feature selection. According to the complexity of the data set, we proposed a comparison of three data imputation methods such as mean imputation (MI), k-nearest neighbor (KNN) and expectation maximization (EM) using mutually the selection of variables technique, whereby t-test, then through the data mining process using logistic regression classification methods, naive Bayes algorithm, linear discriminant analysis and support vector machine hence comparing their respective performances. The experimental results will be spread in developing a model to predict the MSE survival, providing a better understanding in the topic once it is a significant part of the Brazilian' GPA and macroeconomy.

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty estimates. Classical Monte Carlo methods, particularly Markov Chain Monte Carlo, remain the gold standard for approximate Bayesian inference because they have a robust finite-sample theory and reliable convergence diagnostics. However, alternative methods, which are more scalable or apply to problems where Markov Chain Monte Carlo cannot be used, lack the same finite-data approximation theory and tools for evaluating their accuracy. In this work, we develop a flexible new approach to bounding the error of mean and uncertainty estimates of scalable inference algorithms. Our strategy is to control the estimation errors in terms of Wasserstein distance, then bound the Wasserstein distance via a generalized notion of Fisher distance. Unlike computing the Wasserstein distance, which requires access to the normalized posterior distribution, the Fisher distance is tractable to compute because it requires access only to the gradient of the log posterior density. We demonstrate the usefulness of our Fisher distance approach by deriving bounds on the Wasserstein error of the Laplace approximation and Hilbert coresets. We anticipate that our approach will be applicable to many other approximate inference methods such as the integrated Laplace approximation, variational inference, and approximate Bayesian computation

In this work, we developed a network inference method from incomplete data ("PathInf") , as massive and non-uniformly distributed missing values is a common challenge in practical problems. PathInf is a two-stages inference model. In the first stage, it applies a data summarization model based on maximum likelihood to deal with the massive distributed missing values by transforming the observation-wise items in the data into state matrix. In the second stage, transition pattern (i.e. pathway) among variables is inferred as a graph inference problem solved by greedy algorithm with constraints. The proposed method was validated and compared with the state-of-art Bayesian network method on the simulation data, and shown consistently superior performance. By applying the PathInf on the lymph vascular metastasis data, we obtained the holistic pathways of the lymph node metastasis with novel discoveries on the jumping metastasis among nodes that are physically apart. The discovery indicates the possible presence of sentinel node groups in the lung lymph nodes which have been previously speculated yet never found. The pathway map can also improve the current dissection examination protocol for better individualized treatment planning, for higher diagnostic accuracy and reducing the patients trauma.

The human mind is a powerful multifunctional knowledge storage and management system that performs generalization, type inference, anomaly detection, stereotyping, and other tasks. A dynamic KR system that appropriately profiles over sparse inputs to provide complete expectations for unknown facets can help with all these tasks. In this paper, we introduce the task of profiling, inspired by theories and findings in social psychology about the potential of profiles for reasoning and information processing. We describe two generic state-of-the-art neural architectures that can be easily instantiated as profiling machines to generate expectations and applied to any kind of knowledge to fill gaps. We evaluate these methods against Wikidata and crowd expectations, and compare the results to gain insight in the nature of knowledge captured by various profiling methods. We make all code and data available to facilitate future research.

Cyber-physical systems (CPSs) embed software into the physical world. They appear in a wide range of applications such as smart grids, robotics, intelligent manufacture and medical monitoring. CPSs have proved resistant to modeling due to their intrinsic complexity arising from the combination of physical components and cyber components and the interaction between them. This study proposes a general framework for reverse engineering CPSs directly from data. The method involves the identification of physical systems as well as the inference of transition logic. It has been applied successfully to a number of real-world examples ranging from mechanical and electrical systems to medical applications. The novel framework seeks to enable researchers to make predictions concerning the trajectory of CPSs based on the discovered model. Such information has been proven essential for the assessment of the performance of CPS, the design of failure-proof CPS and the creation of design guidelines for new CPSs.