MDL Convergence Speed for Bernoulli Sequences

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.Comment: 28 page

Disentangling Genetic and Prenatal Maternal Effects on Offspring Size and Survival

This is the author accepted manuscript. The final version is available from University of Chicago Press via the DOI in this record.Organizational processes during prenatal development can have long-term effects on an individual's phenotype. Because these early developmental stages are sensitive to environmental influences, mothers are in a unique position to alter their offspring's phenotype by differentially allocating resources to their developing young. However, such prenatal maternal effects are difficult to disentangle from other forms of parental care, additive genetic effects, and/or other forms of maternal inheritance, hampering our understanding of their evolutionary consequences. Here we used divergent selection lines for high and low prenatal maternal investment and their reciprocal line crosses in a precocial bird-the Japanese quail (Coturnix japonica)-to quantify the relative importance of genes and prenatal maternal effects in shaping offspring phenotype. Maternal but not paternal origin strongly affected offspring body size and survival throughout development. Although the effects of maternal egg investment faded over time, they were large at key life stages. Additionally, there was evidence for other forms of maternal inheritance affecting offspring phenotype at later stages of development. Our study is among the first to successfully disentangle prenatal maternal effects from all other sources of confounding variation and highlights the important role of prenatal maternal provisioning in shaping offspring traits closely linked to fitness.The study was financially supported by the Swiss National Science Foundation (PP00P3_128386 and PP00P3_157455 to B.T.)

Probabilities on Sentences in an Expressive Logic

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.Comment: 52 LaTeX pages, 64 definiton/theorems/etc, presented at conference Progic 2011 in New Yor

Self-Modification of Policy and Utility Function in Rational Agents

Any agent that is part of the environment it interacts with and has versatile actuators (such as arms and fingers), will in principle have the ability to self-modify -- for example by changing its own source code. As we continue to create more and more intelligent agents, chances increase that they will learn about this ability. The question is: will they want to use it? For example, highly intelligent systems may find ways to change their goals to something more easily achievable, thereby `escaping' the control of their designers. In an important paper, Omohundro (2008) argued that goal preservation is a fundamental drive of any intelligent system, since a goal is more likely to be achieved if future versions of the agent strive towards the same goal. In this paper, we formalise this argument in general reinforcement learning, and explore situations where it fails. Our conclusion is that the self-modification possibility is harmless if and only if the value function of the agent anticipates the consequences of self-modifications and use the current utility function when evaluating the future.Comment: Artificial General Intelligence (AGI) 201

The \^G Search for Extraterrestrial Civilizations with Large Energy Supplies. IV. The Signatures and Information Content of Transiting Megastructures

Arnold (2005), Forgan (2013), and Korpela et al. (2015) noted that planet-sized artificial structures could be discovered with Kepler as they transit their host star. We present a general discussion of transiting megastructures, and enumerate ten potential ways their anomalous silhouettes, orbits, and transmission properties would distinguish them from exoplanets. We also enumerate the natural sources of such signatures. Several anomalous objects, such as KIC 12557548 and CoRoT-29, have variability in depth consistent with Arnold's prediction and/or an asymmetric shape consistent with Forgan's model. Since well motivated physical models have so far provided natural explanations for these signals, the ETI hypothesis is not warranted for these objects, but they still serve as useful examples of how nonstandard transit signatures might be identified and interpreted in a SETI context. Boyajian et al. 2015 recently announced KIC 8462852, an object with a bizarre light curve consistent with a "swarm" of megastructures. We suggest this is an outstanding SETI target. We develop the normalized information content statistic $M$ to quantify the information content in a signal embedded in a discrete series of bounded measurements, such as variable transit depths, and show that it can be used to distinguish among constant sources, interstellar beacons, and naturally stochastic or artificial, information-rich signals. We apply this formalism to KIC 12557548 and a specific form of beacon suggested by Arnold to illustrate its utility.Comment: 25 pages, 10 figures. Accepted to Ap

Time variation of Kepler transits induced by stellar spots - a way to distinguish between prograde and retrograde motion. II. Application to KOIs

Mazeh, Holczer, and Shporer (2015) have presented an approach that can, in principle, use the derived transit timing variation (TTV) of some transiting planets observed by the $Kepler$ mission to distinguish between prograde and retrograde motion of their orbits with respect to their parent stars' rotation. The approach utilizes TTVs induced by spot-crossing events that occur when the planet moves across a spot on the stellar surface, looking for a correlation between the derived TTVs and the stellar brightness derivatives at the corresponding transits. This can work even in data that cannot temporally resolve the spot-crossing events themselves. Here we apply this approach to the $Kepler$ KOIs, identifying nine systems where the photometric spot modulation is large enough and the transit timing accurate enough to allow detection of a TTV-brightness-derivatives correlation. Of those systems five show highly significant prograde motion (Kepler-17b, Kepler-71b, KOI-883.01, KOI-895.01, and KOI-1074.01), while no system displays retrograde motion, consistent with the suggestion that planets orbiting cool stars have prograde motion. All five systems have impact parameter $0.2\lesssim b\lesssim0.5$, and all systems within that impact parameter range show significant correlation, except HAT-P-11b where the lack of a correlation follows its large stellar obliquity. Our search suffers from an observational bias against detection of high impact parameter cases, and the detected sample is extremely small. Nevertheless, our findings may suggest that stellar spots, or at least the larger ones, tend to be located at a low stellar latitude, but not along the stellar equator, similar to the Sun.Comment: V2: accepted to Ap

Electron-phonon interaction in the solid form of the smallest fullerene C20_{20}

The electron-phonon coupling of a theoretically devised carbon phase made by assembling the smallest fullerenes C$_{20}$ is calculated from first principles. The structure consists of C$_{20}$ cages in an {\it fcc} lattice interlinked by two bridging carbon atoms in the interstitial tetrahedral sites ({\it fcc}-C$_{22}$). The crystal is insulating but can be made metallic by doping with interstitial alkali atoms. In the compound NaC$_{22}$ the calculated coupling constant $\lambda/N(0)$ is 0.28 eV, a value much larger than in C$_{60}$, as expected from the larger curvature of C$_{20}$. On the basis of the McMillan's formula, the calculated $\lambda$=1.12 and a $\mu^*$ assumed in the range 0.3-0.1 a superconducting T$_c$ in the range 15-55 K is predicted.Comment: 7 page

AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs