Automatic Bayesian Density Analysis

Making sense of a dataset in an automatic and unsupervised fashion is a challenging problem in statistics and AI. Classical approaches for {exploratory data analysis} are usually not flexible enough to deal with the uncertainty inherent to real-world data: they are often restricted to fixed latent interaction models and homogeneous likelihoods; they are sensitive to missing, corrupt and anomalous data; moreover, their expressiveness generally comes at the price of intractable inference. As a result, supervision from statisticians is usually needed to find the right model for the data. However, since domain experts are not necessarily also experts in statistics, we propose Automatic Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible at large. Specifically, ABDA allows for automatic and efficient missing value estimation, statistical data type and likelihood discovery, anomaly detection and dependency structure mining, on top of providing accurate density estimation. Extensive empirical evidence shows that ABDA is a suitable tool for automatic exploratory analysis of mixed continuous and discrete tabular data.Comment: In proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19

Bayesian Learning of Sum-Product Networks

Sum-product networks (SPNs) are flexible density estimators and have received significant attention due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be desired: Even though there is a plethora of SPN structure learners, most of them are somewhat ad-hoc and based on intuition rather than a clear learning principle. In this paper, we introduce a well-principled Bayesian framework for SPN structure learning. First, we decompose the problem into i) laying out a computational graph, and ii) learning the so-called scope function over the graph. The first is rather unproblematic and akin to neural network architecture validation. The second represents the effective structure of the SPN and needs to respect the usual structural constraints in SPN, i.e. completeness and decomposability. While representing and learning the scope function is somewhat involved in general, in this paper, we propose a natural parametrisation for an important and widely used special case of SPNs. These structural parameters are incorporated into a Bayesian model, such that simultaneous structure and parameter learning is cast into monolithic Bayesian posterior inference. In various experiments, our Bayesian SPNs often improve test likelihoods over greedy SPN learners. Further, since the Bayesian framework protects against overfitting, we can evaluate hyper-parameters directly on the Bayesian model score, waiving the need for a separate validation set, which is especially beneficial in low data regimes. Bayesian SPNs can be applied to heterogeneous domains and can easily be extended to nonparametric formulations. Moreover, our Bayesian approach is the first, which consistently and robustly learns SPN structures under missing data.Comment: NeurIPS 2019; See conference page for supplemen

Bayesian Structure and Parameter Learning of Sum-Product Networks

Sum-product networks (SPN) are graphical models capable of handling large amount of multi- dimensional data. Unlike many other graphical models, SPNs are tractable if certain structural requirements are fulfilled; a model is called tractable if probabilistic inference can be performed in a polynomial time with respect to the size of the model. The learning of SPNs can be separated into two modes, parameter and structure learning. Many earlier approaches to SPN learning have treated the two modes as separate, but it has been found that by alternating between these two modes, good results can be achieved. One example of this kind of algorithm was presented by Trapp et al. in an article Bayesian Learning of Sum-Product Networks (NeurIPS, 2019). This thesis discusses SPNs and a Bayesian learning algorithm developed based on the earlier men- tioned algorithm, differing in some of the used methods. The algorithm by Trapp et al. uses Gibbs sampling in the parameter learning phase, whereas here Metropolis-Hasting MCMC is used. The algorithm developed for this thesis was used in two experiments, with a small and simple SPN and with a larger and more complex SPN. Also, the effect of the data set size and the complexity of the data was explored. The results were compared to the results got from running the original algorithm developed by Trapp et al. The results show that having more data in the learning phase makes the results more accurate as it is easier for the model to spot patterns from a larger set of data. It was also shown that the model was able to learn the parameters in the experiments if the data were simple enough, in other words, if the dimensions of the data contained only one distribution per dimension. In the case of more complex data, where there were multiple distributions per dimension, the struggle of the computation was seen from the results

PClean: Bayesian Data Cleaning at Scale with Domain-Specific Probabilistic Programming

Data cleaning is naturally framed as probabilistic inference in a generative model, combining a prior distribution over ground-truth databases with a likelihood that models the noisy channel by which the data are filtered, corrupted, and joined to yield incomplete, dirty, and denormalized datasets. Based on this view, we present PClean, a unified generative modeling architecture for cleaning and normalizing dirty data in diverse domains. Given an unclean dataset and a probabilistic program encoding relevant domain knowledge, PClean learns a structured representation of the data as a relational database of interrelated objects, and uses this latent structure to impute missing values, identify duplicates, detect errors, and propose corrections in the original data table. PClean makes three modeling and inference contributions: (i) a domain-general non-parametric generative model of relational data, for inferring latent objects and their network of latent connections; (ii) a domain-specific probabilistic programming language, for encoding domain knowledge specific to each dataset being cleaned; and (iii) a domain-general inference engine that adapts to each PClean program by constructing data-driven proposals used in sequential Monte Carlo and particle Gibbs. We show empirically that short (< 50-line) PClean programs deliver higher accuracy than state-of-the-art data cleaning systems based on machine learning and weighted logic; that PClean's inference algorithm is faster than generic particle Gibbs inference for probabilistic programs; and that PClean scales to large real-world datasets with millions of rows.Comment: Added references; revised abstrac

Tractable Probabilistic Graph Representation Learning with Graph-Induced Sum-Product Networks

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries.Comment: The 12th International Conference on Learning Representations (ICLR 2024