**Generative Adversarial Imitation Learning (GAIL)**

… **Dodgson Score**

Dodgson’s method is a voting system proposed by the author, mathematician and logician Charles Dodgson, better known as Lewis Carroll. The method is to extend the Condorcet method by swapping candidates until a Condorcet winner is found. The winner is the candidate which requires the minimum number of swaps. Dodgson proposed this voting scheme in his 1876 work ‘A method of taking votes on more than two issues’. Given an integer k and an election, it is NP-complete to determine whether or not a candidate can become a Condorcet winner with fewer than k swaps. In Dodgson’s method, each voter submits an ordered list of all candidates according to their own preference (from best to worst). The winner is defined to be the candidate for whom we need to perform the minimum number of pairwise swaps (added over all candidates) before they become a Condorcet winner. In particular, if there is already a Condorcet winner, they win the election. In short, we must find the voting profile with minimum Kendall tau distance from the input, such that it has a Condorcet winner; they are declared the victor. Computing the winner or even the Dodgson score of a candidate (the number of swaps needed to make him a winner) is a PNP||-complete problem.

Efficient Dodgson-Score Calculation Using Heuristics and Parallel Computing … **Sampled Weighted Min-Hashing (SWMH)**

We present Sampled Weighted Min-Hashing (SWMH), a randomized approach to automatically mine topics from large-scale corpora. SWMH generates multiple random partitions of the corpus vocabulary based on term co-occurrence and agglomerates highly overlapping inter-partition cells to produce the mined topics. While other approaches define a topic as a probabilistic distribution over a vocabulary, SWMH topics are ordered subsets of such vocabulary. Interestingly, the topics mined by SWMH underlie themes from the corpus at different levels of granularity. We extensively evaluate the meaningfulness of the mined topics both qualitatively and quantitatively on the NIPS (1.7 K documents), 20 Newsgroups (20 K), Reuters (800 K) and Wikipedia (4 M) corpora. Additionally, we compare the quality of SWMH with Online LDA topics for document representation in classification. …

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**30**
*Monday*
Oct 2017

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