Learning about meetings

Abstract

Most people participate in meetings almost every day, multiple times a day. The study of meetings is important, but also challenging, as it requires an understanding of social signals and complex interpersonal dynamics. Our aim in this work is to use a data-driven approach to the science of meetings. We provide tentative evidence that: (i) it is possible to automatically detect when during the meeting a key decision is taking place, from analyzing only the local dialogue acts, (ii) there are common patterns in the way social dialogue acts are interspersed throughout a meeting, (iii) at the time key decisions are made, the amount of time left in the meeting can be predicted from the amount of time that has passed, (iv) it is often possible to predict whether a proposal during a meeting will be accepted or rejected based entirely on the language (the set of persuasive words) used by the speaker.

Appendix: Proof of Theorem 1

We will use Hoeffding’s inequality combined with the union bound to create a uniform generalization bound over all viable templates. The main step in doing this is to count the number of possible viable templates. Let us do this now.

Let $\Lambda$ be the set of possible dialogue acts, and denote $|\Lambda |$ as the number of elements in the set. We will calculate the number of templates that are of size less than or equal to $L$, which is the size of our function class in statistical learning theory.

For a template of exactly length $n$, there are $|\Lambda |^n$ possible assignments of dialogue acts for the templates. Also, for a template of length $n$, there are at most ${n(n-1)/2 \atopwithdelims ()B}$ possible assignments of $B$ backward arrows, where $B \le n$. To see this, consider the set of backwards arrows as represented by an $n\times n$ adjacency matrix, where only the part below the diagonal could be 1. There are $n^2$ total elements in the matrix, $n$ on the diagonal, so $n(n-1)$ off diagonal elements, and $n(n-1)/2$ elements in the lower triangle. If exactly $b$ of these can be 1, the total number of possibilities is at most ${n(n-1)/2 \atopwithdelims ()b}$. There can be up to $B$ backward arrows, so the total number of possibilities is at most

$$\begin{aligned} \sum _{b=0}^{\min (B,n)} {n(n-1)/2 \atopwithdelims ()b}. \end{aligned}$$

Note that this number is an upper bound, as usually we cannot have more than one backwards arrow leaving or entering a node. Finally we could have $n$ anywhere between 0 and $L$ so the final number of possible templates has upper bound:

$$\begin{aligned} \sum _{n=0}^{L} |\Lambda |^n \sum _{b=0}^{\min (B,n)} {n(n-1)/2 \atopwithdelims ()b}. \end{aligned}$$

Hoeffding’s inequality applies to arbitrary bounded loss functions. This, combined with a union bound over all viable templates, yields the statement of the theorem.