Group Equivariant Capsule Network google
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. We restrict pose vectors and learned transformations to be elements of a group, which allows us to prove equivariance of pose vectors and invariance of activations under application of the group law. Requirements are a modified spatial aggregation method for capsules and a generic routing by agreement algorithm with abstract rules, which we both present in this work. Further, we connect our equivariant capsule networks with work from the field of group convolutional networks, which consist of convolutions that are equivariant under applications of the group law. Through this connection, we are able to provide intuitions of how both methods relate and are able to combine both approaches in one deep neural network architecture, combining the strengths from both fields. The resulting framework allows sparse evaluation of feature maps defined over groups, provides control over specific equivariance and invariance properties and can use routing by agreement instead of pooling operations. It provides interpretable and equivariant representation vectors as output capsules, which disentangle evidence of object existence from its pose. …

Parallel Coordinates google
Parallel coordinates is a common way of visualizing high-dimensional geometry and analyzing multivariate data. To show a set of points in an n-dimensional space, a backdrop is drawn consisting of n parallel lines, typically vertical and equally spaced. A point in n-dimensional space is represented as a polyline with vertices on the parallel axes; the position of the vertex on the ith axis corresponds to the ith coordinate of the point. This visualization is closely related to time series visualization, except that it is applied to data where the axes do not correspond to points in time, and therefore do not have a natural order. Therefore, different axis arrangements may be of interest. …

VerdictDB google
Despite 25 years of research in academia, approximate query processing (AQP) has had little industrial adoption. One of the major causes for this slow adoption is the reluctance of traditional vendors to make radical changes to their legacy codebases, and the preoccupation of newer vendors (e.g., SQL-on-Hadoop products) with implementing standard features. On the other hand, the few AQP engines that are available are each tied to a specific platform and require users to completely abandon their existing databases—an unrealistic expectation given the infancy of the AQP technology. Therefore, we argue that a universal solution is needed: a database-agnostic approximation engine that will widen the reach of this emerging technology across various platforms. Our proposal, called VerdictDB, uses a middleware architecture that requires no changes to the backend database, and thus, can work with all off-the-shelf engines. Operating at the driver-level, VerdictDB intercepts analytical queries issued to the database and rewrites them into another query that, if executed by any standard relational engine, will yield sufficient information for computing an approximate answer. VerdictDB uses the returned result set to compute an approximate answer and error estimates, which are then passed on to the user or application. However, lack of access to the query execution layer introduces significant challenges in terms of generality, correctness, and efficiency. This paper shows how VerdictDB overcomes these challenges and delivers up to 171 times speedup (18.45 times on average) for a variety of existing engines, such as Impala, Spark SQL, and Amazon Redshift while incurring less than 2.6% relative error. …

Kalman Optimization for Value Approximation (KOVA) google
Policy evaluation is a key process in reinforcement learning. It assesses a given policy using estimation of the corresponding value function. When using a parameterized function to approximate the value, it is common to optimize the set of parameters by minimizing the sum of squared Bellman Temporal Differences errors. However, this approach ignores certain distributional properties of both the errors and value parameters. Taking these distributions into account in the optimization process can provide useful information on the amount of confidence in value estimation. In this work we propose to optimize the value by minimizing a regularized objective function which forms a trust region over its parameters. We present a novel optimization method, the Kalman Optimization for Value Approximation (KOVA), based on the Extended Kalman Filter. KOVA minimizes the regularized objective function by adopting a Bayesian perspective over both the value parameters and noisy observed returns. This distributional property provides information on parameter uncertainty in addition to value estimates. We provide theoretical results of our approach and analyze the performance of our proposed optimizer on domains with large state and action spaces. …