Greedy Algorithms for Optimal Distribution Approximation

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which is an appropriate measure, e.g., in the context of data compression. Properties of the optimal approximation are derived and bounds on the approximation error are presented, which are asymptotically tight. It is shown that $M$-type approximations that minimize either $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, or $\mathbb{D}(\mathbf{p}\Vert\mathbf{t})$, or the variational distance $\Vert\mathbf{p}-\mathbf{t}\Vert_1$ can all be found by using specific instances of the same general greedy algorithm.Comment: 5 page

Magnetoresistance Effects in SrFeO(3-x): Dependence on Phase Composition and Relation to Magnetic and Charge Order

Single crystals of iron(IV) rich oxides SrFeO(3-x) with controlled oxygen content have been studied by Moessbauer spectroscopy, magnetometry, magnetotransport measurements, Raman spectroscopy, and infrared ellipsometry in order to relate the large magnetoresistance (MR) effects in this system to phase composition, magnetic and charge order. It is shown that three different types of MR effects occur. In cubic SrFeO3 (x = 0) a large negative MR of 25% at 9 T is associated with a hitherto unknown 60 K magnetic transition and a subsequent drop in resistivity. The 60 K transition appears in addition to the onset of helical ordering at ~130 K. In crystals with vacancy-ordered tetragonal SrFeO(3-x) as majority phase (x ~0.15) a coincident charge/antiferromagnetic ordering transition near 70 K gives rise to a negative giant MR effect of 90% at 9 T. A positive MR effect is observed in tetragonal and orthorhombic materials with increased oxygen deficiency (x = 0.19, 0.23) which are insulating at low temperatures. Phase mixtures can result in a complex superposition of these different MR phenomena. The MR effects in SrFeO(3-x) differ from those in manganites as no ferromagnetic states are involved

Optimal Kullback-Leibler Aggregation via Information Bottleneck

In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost; The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a sub-optimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.Comment: 13 pages, 4 figure