题目一：Reasoning with belief functions: a deductive approach

报告人：周春来

时间：7月26日下午14点整

地点：信息楼417室

摘要：The theory of belief functions has become a popular tool in AI for
the representation of knowledge.   Usually belief functions are
nonnegative monotonic functions defined on Boolean algebras of events.
 In this talk, I will extend this theory to sets of events that are
not structured as Boolean algebras but as distributive lattices.
With this generalized mathematical theory,  I investigate a deductive
approach to reasoning with belief functions in nonclassical cases when
the knowledge base may be inconsistent or incomplete.  At the end of
this talk, I will connect this approach to reasoning with
probabilities.

题目二：A null space tuning algorithm for sparse representation

报告人：密铁宾

时间：7月26日下午15点

地点：信息楼417室

摘要：Based on proper null space tuning, we provide an iterative
framework for sparse representations of the form of $Ax = f$, where
columns of $A$ is a frame system in $\mathbb{C}^n$.  It is well-known
that by using the dual frame formula, a sequence of solutions
$\{x_{n}\}$ to $Ax = f$ can be generated by the iteration,
\[
x_{n+1} = x_{n} + Hb, \quad \ n=0,1,\ldots,
\]
where $H = I - A^* (A A^*)^{-1} A $ is a projection onto the null
space of $A$ and $b$ is a free vector. We present some strategies in
the null space tuning that give rise to extremely efficient iterative
algorithms.  These algorithms can also be used to recover sparse
signal in compressed sensing. This framework possesses an intuitive
geometric interpretation, which has not been exploited in the past.
Various iterative thresholding algorithms proposed by other scholars
can be shown to be part of this fundamental framework. In particular,
with this framework, we may also obtain an adaptive dual frame
$\tilde{A}$ of $A$ such that $\tilde{A}^* f$ is the sparse
representation coefficients.   This is a joint work with Shidong Li
and Yulong Liu.