From Stochastic Mixability to Fast Rates

Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class $\mathcal{F}$ with small loss $\ell$. In the parametric setting, depending upon $(\ell, \mathcal{F},\mathsf{P})$ ERM can have slow $(1/\sqrt{n})$ or fast $(1/n)$ rates of convergence of the excess risk as a function of the sample size $n$. There exist several results that give sufficient conditions for fast rates in terms of joint properties of $\ell$, $\mathcal{F}$, and $\mathsf{P}$, such as the margin condition and the Bernstein condition. In the non-statistical prediction with expert advice setting, there is an analogous slow and fast rate phenomenon, and it is entirely characterized in terms of the mixability of the loss $\ell$ (there being no role there for $\mathcal{F}$ or $\mathsf{P}$). The notion of stochastic mixability builds a bridge between these two models of learning, reducing to classical mixability in a special case. The present paper presents a direct proof of fast rates for ERM in terms of stochastic mixability of $(\ell,\mathcal{F}, \mathsf{P})$, and in so doing provides new insight into the fast-rates phenomenon. The proof exploits an old result of Kemperman on the solution to the general moment problem. We also show a partial converse that suggests a characterization of fast rates for ERM in terms of stochastic mixability is possible.Comment: 21 pages, accepted to NIPS 201

Particle Filter Design Using Importance Sampling for Acoustic Source Localisation and Tracking in Reverberant Environments

Sequential Monte Carlo methods have been recently proposed to deal with the problem of acoustic source localisation and tracking using an array of microphones. Previous implementations make use of the basic bootstrap particle filter, whereas a more general approach involves the concept of importance sampling. In this paper, we develop a new particle filter for acoustic source localisation using importance sampling, and compare its tracking ability with that of a bootstrap algorithm proposed previously in the literature. Experimental results obtained with simulated reverberant samples and real audio recordings demonstrate that the new algorithm is more suitable for practical applications due to its reinitialisation capabilities, despite showing a slightly lower average tracking accuracy. A real-time implementation of the algorithm also shows that the proposed particle filter can reliably track a person talking in real reverberant rooms.This paper was performed while Eric A. Lehmann was working with National ICT Australia. National ICT Australia is funded by the Australian Government’s Department of Communications, Information Technology, and the Arts, the Australian Research Council, through Backing Australia’s Ability, and the ICT Centre of Excellence programs

Interface design in the process industries

Every operator runs his plant in accord with his own mental model of the process. In this sense, one characteristic of an ideal man-machine interface is that it be in harmony with that model. With this theme in mind, the paper first reviews the functions of the process operator and compares them with human operators involved in control situations previously studied outside the industrial environment (pilots, air traffic controllers, helmsmen, etc.). A brief history of the operator interface in the process industry and the traditional methodology employed in its design is then presented. Finally, a much more fundamental approach utilizing a model definition of the human operator's behavior is presented

Anxious to see you: Neuroendocrine mechanisms of social vigilance and anxiety during adolescence.

Social vigilance is a behavioral strategy commonly used in adverse or changing social environments. In animals, a combination of avoidance and vigilance allows an individual to evade potentially dangerous confrontations while monitoring the social environment to identify favorable changes. However, prolonged use of this behavioral strategy in humans is associated with increased risk of anxiety disorders, a major burden for human health. Elucidating the mechanisms of social vigilance in animals could provide important clues for new treatment strategies for social anxiety. Importantly, during adolescence the prevalence of social anxiety increases significantly. We hypothesize that many of the actions typically characterized as anxiety behaviors begin to emerge during this time as strategies for navigating more complex social structures. Here, we consider how the social environment and the pubertal transition shape neural circuits that modulate social vigilance, focusing on the bed nucleus of the stria terminalis and prefrontal cortex. The emergence of gonadal hormone secretion during adolescence has important effects on the function and structure of these circuits, and may play a role in the emergence of a notable sex difference in anxiety rates across adolescence. However, the significance of these changes in the context of anxiety is still uncertain, as not enough studies are sufficiently powered to evaluate sex as a biological variable. We conclude that greater integration between human and animal models will aid the development of more effective strategies for treating social anxiety

Composite Geometric Phase for Multipartite Entangled States

When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical phases of its subsystems. In contrast, the equivalent statement for the geometric phase is not generally true unless the state is separable. For an entangled state an additional term is present, the mutual geometric phase, that measures the change the additional correlations present in the entangled state make to the geometry of the state space. For $N$ qubit states we find this change can be explained solely by classical correlations for states with a Schmidt decomposition and solely by quantum correlations for W states.Comment: 4 pages, 1 figure, improved presentation, results and conclusions unchanged from v1. Accepted for publication in PR

Cheating at Craps: A Quantitative Analysis

Craps is a simple dice game that is popular in casinos around the world. While the rules for Craps, and its mathematical analysis, are reasonably straightforward, this paper instead focuses on the best ways to cheat at Craps, by using loaded (biased) dice. We use both analytical modeling and simulation modeling to study this intriguing dice game. Our modeling results show that biasing a die away from the value 1 or towards the value 5 lead to the best (and least detectable) cheating strategies, and that modest bias on two loaded dice can increase the winning probability above 50%. Our Monte Carlo simulation results provide validation for our analytical model, and also facilitate the quantitative evaluation of other scenarios, such as heterogeneous or correlated dice

Comparison of two methods for describing the strain profiles in quantum dots

The electronic structure of interfaces between lattice-mismatched semiconductor is sensitive to the strain. We compare two approaches for calculating such inhomogeneous strain -- continuum elasticity (CE, treated as a finite difference problem) and atomistic elasticity (AE). While for small strain the two methods must agree, for the large strains that exist between lattice-mismatched III-V semiconductors (e.g. 7% for InAs/GaAs outside the linearity regime of CE) there are discrepancies. We compare the strain profile obtained by both approaches (including the approximation of the correct C_2 symmetry by the C_4 symmetry in the CE method), when applied to C_2-symmetric InAs pyramidal dots capped by GaAs.Comment: To appear in J. Appl. Physic

Phosphate availability regulates root system architecture in Arabidopsis

Plant root systems are highly plastic in their development and can adapt their architecture in response to the prevailing environmental conditions. One important parameter is the availability of phosphate, which is highly immobile in soil such that the arrangement of roots within the soil will profoundly affect the ability of the plant to acquire this essential nutrient. Consistent with this, the availability of phosphate was found to have a marked effect on the root system architecture of Arabidopsis. Low phosphate availability favored lateral root growth over primary root growth, through increased lateral root density and length, and reduced primary root growth mediated by reduced cell elongation. The ability of the root system to respond to phosphate availability was found to be independent of sucrose supply and auxin signaling. In contrast, shoot phosphate status was found to influence the root system architecture response to phosphate availability

Nitrate and phosphate availability and distribution have different effects on root system architecture of Arabidopsis

Plant root systems can respond to nutrient availability and distribution by changing the three-dimensional deployment of their roots: their root system architecture (RSA). We have compared RSA in homogeneous and heterogeneous nitrate and phosphate supply in Arabidopsis. Changes in nitrate and phosphate availability were found to have contrasting effects on primary root length and lateral root density, but similar effects on lateral root length. Relative to shoot dry weight (DW), primary root length decreased with increasing nitrate availability, while it increased with increasing phosphate supply. Lateral root density remained constant across a range of nitrate supplies, but decreased with increasing phosphate supply. In contrast, lateral root elongation was suppressed both by high nitrate and high phosphate supplies. Local supplies of high nitrate or phosphate in a patch also had different effects. Primary root growth was not affected by a high nitrate patch, but growth through a high phosphate patch reduced primary root growth after the root left the patch. A high nitrate patch induced an increase in lateral root density in the patch, whereas lateral root density was unaffected by a high phosphate patch. However, both phosphate- and nitrate-rich patches induced lateral root elongation in the patch and suppressed it outside the patch. This co-ordinated response of lateral roots also occurs in soil-grown plants exposed to a nutrient-rich patch. The auxin-resistant mutants axr1, axr4 and aux1 all showed the wild-type lateral root elongation responses to a nitrate-rich patch, suggesting that auxin is not required for this response