Capsule networks (see Hinton et al., 2018) aim to encode knowledge of and reason about the relationship between an object and its parts. In this letter, we specify a generative model for such data and derive a variational algorithm for inferring the transformation of each model object in a scene and the assignments of observed parts to the objects. We derive a learning algorithm for the object models, based on variational expectation maximization (Jordan et al., 1999). We also study an alternative inference algorithm based on the RANSAC method of Fischler and Bolles (1981). We apply these inference methods to data generated from multiple geometric objects like squares and triangles ("constellations") and data from a parts-based model of faces. Recent work by Kosiorek et al. (2019) has used amortized inference via stacked capsule autoencoders to tackle this problem; our results show that we significantly outperform them where we can make comparisons (on the constellations data).

Data wrangling tasks such as obtaining and linking data from various sources, transforming data formats, and correcting erroneous records, can constitute up to 80% of typical data engineering work. Despite the rise of machine learning and artificial intelligence, data wrangling remains a tedious and manual task. We introduceAI assistants, a class of semi-automatic interactive tools to streamline data wrangling. An AI assistant guides the analyst through a specific data wrangling task by recommending a suitable data transformation that respects the constraints obtained through interaction with the analyst. We formally define the structure of AI assistants and describe how existing tools that treat data cleaning as an optimization problem fit the definition. We implement AI assistants for four common data wrangling tasks and make AI assistants easily accessible to data analysts in an open-source notebook environment for data science, by leveraging the common structure they follow. We evaluate our AI assistants both quantitatively and qualitatively through three example scenarios. We show that the unified and interactive design makes it easy to perform tasks that would be difficult to do manually or with a fully automatic tool.

We focus on the problem of unsupervised cell outlier detection and repair inmixed-type tabular data. Traditional methods are concerned only with detecting which rows in the dataset areoutliers. However, identifying which cells are corrupted in aspecific row is an important problem in practice, and the very first steptowards repairing them. We introduce the Robust VariationalAutoencoder (RVAE), a deep generative model that learns the jointdistribution of the clean data while identifying the outlier cells, allowing their imputation (repair). RVAE explicitly learns the probability of each cell being an outlier, balancing differentlikelihood models in the row outlier score, making the method suitablefor outlier detection in mixed-type datasets.We show experimentallythat not only RVAE performs better than several state-of-the-art methods incell outlier detection and repair for tabular data, but also that is robust against theinitial hyper-parameter selection.

We consider the problem of daily human activity recognition (HAR) using multiple wireless inertial sensors, and specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first-order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semisupervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and an Markovian structure of the human activities.

Hidden Markov Models (HMMs) are one of the most important techniques to model and classify sequential data. Maximum Likelihood (ML) and (parametric and non-parametric) Bayesian estimation of the HMM parameters suffers from local maxima and in massive datasets they can be specially time consuming. In this paper, we extend the spectral learning of HMMs, a moment matching learning technique free from local maxima, to discriminative HMMs. The resulting method provides the posterior probabilities of the classes without explicitly determining the HMM parameters, and is able to deal with missing labels. We apply the method to Human Activity Recognition (HAR) using two different types of sensors: portable inertial sensors, and fixed, wireless binary sensor networks. Our algorithm outperforms the standard discriminative HMM learning in both complexity and accuracy.

The goal of this paper consists in characterizing the capacity region of a broadcast system based on analog antenna combining and orthogonal frequency division multiplexing (OFDM). In particular, we consider the maximization of a weighted sum of the rates, which results in a highly non-convex optimization problem. The proposed iterative approach is based on the alternative optimization of the beamformers, and the power and subcarrier allocation. Finally, our experiments show that in most practical situations, the complexity of the optimal approaches (subcarrier sharing and power allocation) is not justified by the marginal gains in the capacity region.