Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction between random subspaces is negligible with high probability. We demonstrate the feasibility of this approach with experimental results for a new use case -- multitask learning with hundreds of thousands of tasks.
A related construction is the CountMin sketch of @cite_3 which stores counts in a number of replicates of a hash table. This leads to good concentration inequalities for range and point queries.
@cite_3
2131409447 2012005986 1865797552 2561776174
We exploit sketch techniques, especially the Count-Min sketch, a memory, and time efficient framework which approximates the frequency of a word pair in the corpus without explicitly storing the word pair itself. These methods use hashing to deal with massive amounts of streaming text. We apply Count-Min sketch to approximate word pair counts and exhibit their effectiveness on three important NLP tasks. Our experiments demonstrate that on all of the three tasks, we get performance comparable to Exact word pair counts setting and state-of-the-art system. Our method scales to 49 GB of unzipped web data using bounded space of 2 billion counters (8 GB memory). Faced with handling multiple large data sets in modern data-processing settings, researchers have proposed sketch data structures that capture salient properties while occupying little memory and that update or probe quickly. In particular, the Count-Min sketch has proven effective for a variety of applications. It concurrently tracks many item counts with surprisingly strong accuracy. We introduce a new sublinear space data structure—the Count-Min Sketch— for summarizing data streams. Our sketch allows fundamental queries in data stream summarization such as point, range, and inner product queries to be approximately answered very quickly; in addition, it can be applied to solve several important problems in data streams such as finding quantiles, frequent items, etc. The time and space bounds we show for using the CM sketch to solve these problems significantly improve those previously known — typically from 1 e 2 to 1 e in factor. Count-based exploration algorithms are known to perform near-optimally when used in conjunction with tabular reinforcement learning (RL) methods for solving small discrete Markov decision processes (MDPs). It is generally thought that count-based methods cannot be applied in high-dimensional state spaces, since most states will only occur once. Recent deep RL exploration strategies are able to deal with high-dimensional continuous state spaces through complex heuristics, often relying on optimism in the face of uncertainty or intrinsic motivation. @PARASPLIT In this work, we describe a surprising finding: a simple generalization of the classic count-based approach can reach near state-of-the-art performance on various high-dimensional and or continuous deep RL benchmarks. States are mapped to hash codes, which allows to count their occurrences with a hash table. These counts are then used to compute a reward bonus according to the classic count-based exploration theory. We find that simple hash functions can achieve surprisingly good results on many challenging tasks. Furthermore, we show that a domain-dependent learned hash code may further improve these results. @PARASPLIT Detailed analysis reveals important aspects of a good hash function: 1) having appropriate granularity and 2) encoding information relevant to solving the MDP. This exploration strategy achieves near state-of-the-art performance on both continuous control tasks and Atari 2600 games, hence providing a simple yet powerful baseline for solving MDPs that require considerable exploration.