Review: [Untitled] Reviewed Work(s):

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available a

Convexity, classification, and risk bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions

Autocyclic behaviour of alluvial and deltaic systems. Geologica Ultraiectina (306)

Strata formation in sedimentary systems is the result of the interplay of controls generated within (autogenic) and outside (allogenic) the system. Allogenic controls include climate, sea level and tectonics. For example, tectonic tilting or sea-level variations can alter the space available for sediments to fill (accommodation), affecting the amount and characteristics of the accumulating sediments. Climate change can influence supply to the system, generating variations in (the rate of) aggradation or degradation. Since the characteristics and relative importance of the autogenic processes are still poorly known and impossible to infer from natural sedimentary systems, analogue experiments have been carried out to unravel the interacting controls. Autogenic evolution was studied separately for three different types of sedimentary systems: alluvial fans, fan deltas and a flood-tidal delta. In each experimental study the allogenic boundary conditions were held constant allowing the systems to grow and evolve in absence of externally imposed variation (base level or input of water and sediment). Autocyclic behaviour (i.e., repetitive autogenic behaviour) of alluvial fans and fan deltas was similar, consisting of alternations of sheet and channelised flow. Channelised flow was initiated by slope-driven incision, and terminated by loss of flow momentum and subsequent channel filling. Flood-tidal delta behaviour deviated from that seen on alluvial fans and fan deltas and showed lateral migration and expansion of tidal channels followed by channel abandonment and filling. All experiments demonstrated that autogenic processes and allogenic variations have a comparable impact on the morphodynamic evolution and, in the case of the alluvial fans and fan deltas, depositional architecture. The autogenic processes on the flood-tidal delta were limited to the intertidal part, and hardly left stratigraphic signals as the migrating tidal channels continuously reworked the remnants of previous channels. In addition, the effect of base level was investigated by comparing the autogenic development of alluvial fans (positioned far from base level) and fan deltas (positioned at a standing body of water, so the shoreline formed its base level). With identical input of water and sediment, alluvial-fan behaviour demonstrated remarkable differences in slope and frequency of autogenic processes, until it reached base level and started acting as a fan delta, substantiating earlier flume and numerical studies. To further apply developed concepts on autocyclic behaviour for Martian fan deltas, a series of fan deltas were formed in a mock-crater mimicking conditions similar to a specific type of deltas (stepped deltas) found on Mars. By comparing the morphology of the experimental and Martian deltas these experiments demonstrated that the Martian deltas were formed in one event of rapid water release, and the steps were generated by the interaction between the rising water level in the crater and autogenic variations in the supply related to processes in the upstream feeder channel