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Yonatan Bilu

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AAAI Conference 2020 Conference Paper

Corpus Wide Argument Mining—A Working Solution

Liat Ein-Dor
Eyal Shnarch
Lena Dankin
Alon Halfon
Benjamin Sznajder
Ariel Gera
Carlos Alzate
Martin Gleize

One of the main tasks in argument mining is the retrieval of argumentative content pertaining to a given topic. Most previous work addressed this task by retrieving a relatively small number of relevant documents as the initial source for such content. This line of research yielded moderate success, which is of limited use in a real-world system. Furthermore, for such a system to yield a comprehensive set of relevant arguments, over a wide range of topics, it requires leveraging a large and diverse corpus in an appropriate manner. Here we present a ﬁrst end-to-end high-precision, corpus-wide argument mining system. This is made possible by combining sentence-level queries over an appropriate indexing of a very large corpus of newspaper articles, with an iterative annotation scheme. This scheme addresses the inherent label bias in the data and pinpoints the regions of the sample space whose manual labeling is required to obtain high-precision among top-ranked candidates.

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FOCS Conference 2004 Conference Paper

Constructing Expander Graphs by 2-Lifts and Discrepancy vs. Spectral Gap

Yonatan Bilu
Nati Linial

We present a new explicit construction for expander graphs with nearly optimal spectral gap. The construction is based on a series of 2-lift operations. Let G be a graph on n vertices. A 2-lift of G is a graph H on 2n vertices, with a covering map /spl pi/: H /spl rarr/ G. It is not hard to see that all eigenvalues of G are also eigenvalues of H. In addition, H has n "new" eigenvalues. We conjecture that every d-regular graph has a 2-lift such that all new eigenvalues are in the range [-2/spl radic/d-1, /spl radic/d-1] (If true, this is tight, e. g. by the Alon-Boppana bound). Here we show that every graph of maximal degree d has a 2-lift such that all "new" eigenvalues are in the range [-c/spl radic/d log/sup 3/d, c/spl radic/d log/sup 3/ d] for some constant c. This leads to a polynomial time algorithm for constructing arbitrarily large d-regular graphs, with second eigenvalue O(/spl radic/d log/sup 3/ d). The proof uses the following lemma (Lemma 3. 6): Let A be a real symmetric matrix with zeros on the diagonal. Let d be such that the l/sub 1/ norm of each row in A is at most d. Suppose that (|xAy|)/(/spl par/x/spl par//spl par/y/spl par/) /spl les/ /spl alpha/ for every x, y /spl isin/ {0, l}/sup n/ with (x, y)= 0. Then the spectral radius of A is O(/spl alpha/(log(d//spl alpha/) + 1)). An interesting consequence of this lemma is a converse to the expander mixing lemma.

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