On Sufficiency and Invariance

Visual Scene Representations: Sufficiency, Minimality, Invariance and Deep Approximation

Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of raw data with smallest complexity and no performance loss on the task at hand. Invariance guarantees that the statistic is constant with respect to uninform...

I . . I I the Relationship between Sufficiency and Invariance with Applications in Sequential Analysis

Φ - Divergences , Sufficiency , Bayes Sufficiency , and Deficiency

The paper studies the relations between φ-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam’s deficiency. A new and considerably simplified approach is given to the spectral representation of φ-divergences already established in Österreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form...

Consciousness and Attention: On Sufficiency and Necessity

Recent research has slowly corroded a belief that selective attention and consciousness are so tightly entangled that they cannot be individually examined. In this review, we summarize psychophysical and neurophysiological evidence for a dissociation between top-down attention and consciousness. The evidence includes recent findings that show subjects can attend to perceptually invisible object...

Sufficiency on the Stock Market

It is well-known that there are a number of relations between theoretical finance theory and information theory. Some of these relations are exact and some are approximate. In this paper we will explore some of these relations and determine under which conditions the relations are exact. It turns out that portfolio theory always leads to Bregman divergences. The Bregman divergence is only propo...