Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a plan) in this graph. While the graphs themselves are represented compactly as planning instances, the paths are usually represented explicitly as sequences of actions. Some cases are known where the plans always have compact representations, for example, using macros. We show that these results do not extend to the general case, by proving a number of bounds for compact representations of plans under various criteria, like efficient sequential or random access of actions. In addition to this, we show that our results have consequences for what can be gained from reformulating planning into some other problem. As a contrast to this we also prove a number of positive results, demonstrating restricted cases where plans do have useful compact representations, as well as proving that macro plans have favourable access properties. Our results are finally discussed in relation to other relevant contexts.
For many classic structured prediction problems, probability distributions over the dependent variables can be efficiently computed using widely-known algorithms and data structures (such as forward-backward, and its corresponding trellis for exact probability distributions in Markov models). However, we know of no previous work studying efficient representations of exact distributions over clusterings. This paper presents definitions and proofs for a dynamic-programming inference procedure that computes the partition function, the marginal probability of a cluster, and the MAP clustering---all exactly. Rather than the Nth Bell number, these exact solutions take time and space proportional to the substantially smaller powerset of N. Indeed, we improve upon the time complexity of the algorithm introduced by Kohonen and Corander (2016) for this problem by a factor of N. While still large, this previously unknown result is intellectually interesting in its own right, makes feasible exact inference for important real-world small data applications (such as medicine), and provides a natural stepping stone towards sparse-trellis approximations that enable further scalability (which we also explore). In experiments, we demonstrate the superiority of our approach over approximate methods in analyzing real-world gene expression data used in cancer treatment.
Biological movement is built up of sub-blocks or motion primitives. Such primitives provide a compact representation of movement which is also desirable in robotic control applications. We analyse handwriting data to gain a better understanding of use of primitives and their timings in biological movements. Inference of the shape and the timing of primitives can be done using a factorial HMM based model, allowing the handwriting to be represented in primitive timing space. This representation provides a distribution of spikes corresponding to the primitive activations, which can also be modelled using HMM architectures.
Getting a robust time-series clustering with best choice of distance measure and appropriate representation is always a challenge. We propose a novel mechanism to identify the clusters combining learned compact representation of time-series, Auto Encoded Compact Sequence (AECS) and hierarchical clustering approach. Proposed algorithm aims to address the large computing time issue of hierarchical clustering as learned latent representation AECS has a length much less than the original length of time-series and at the same time want to enhance its performance.Our algorithm exploits Recurrent Neural Network (RNN) based under complete Sequence to Sequence(seq2seq) autoencoder and agglomerative hierarchical clustering with a choice of best distance measure to recommend the best clustering. Our scheme selects the best distance measure and corresponding clustering for both univariate and multivariate time-series. We have experimented with real-world time-series from UCR and UCI archive taken from diverse application domains like health, smart-city, manufacturing etc. Experimental results show that proposed method not only produce close to benchmark results but also in some cases outperform the benchmark.
As real estate prices soar, tiny homes are becoming more prevalent. If you're thinking about moving into one, there are multiple aspects of your life that you're going to have to scale back, including your laundry. You might have to compromise on size, but getting the right model means you won't have to lose a shred of performance. However, smaller capacity does mean more loads and more time spent doing laundry, but that's a small price to pay to avoid lugging your dirty clothes down to the laundromat. Also, keep in mind that compact washers often require a 220V connection.