arXiv subjects

David Wolpert

Publications and source records attributed to David Wolpert.

32 records · Page 2Linked to original sources

arXiv2018

Constraints on physical reality arising from a formalization of knowledge

There are (at least) four ways that an agent can acquire information concerning the state of the universe: via observation, control, prediction, or via retrodiction, i.e., memory. Each of these four ways of acquiring information seems to rely on a different kind of physical device (resp., an observation device, a control device, etc.). However it turns out that certain mathematical structure is common to those four types of device. Any device that possesses a certain subset of that structure is known as an "inference device" (ID). Here I review some of the properties of IDs, including their relation with Turing machines, and (more loosely) quantum mechanics. I also review the bounds of the joint abilities of any set of IDs to know facts about the physical universe that contains them. These bounds constrain the possible properties of any universe that contains agents who can acquire information concerning that universe. I then extend this previous work on IDs, by adding to the definition of IDs some of the other mathematical structure that is common to the four ways of acquiring information about the universe but is not captured in the (minimal) definition of IDs. I discuss these extensions of IDs in the context of epistemic logic (especially possible worlds formalisms like Kripke structures and Aumann structures). In particular, I show that these extensions of IDs are not subject to the problem of logical omniscience that plagues many previously studied forms of epistemic logic.

physics.hist-ph↗

arXiv2017

Coarse-graining and the Blackwell order

Suppose we have a pair of information channels, $κ_{1},κ_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $κ_{1}$ and $κ_{2}$ by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, $κ_{1}$ is said to be Blackwell-inferior to $κ_{2}$ if and only if $κ_{1}$ can be constructed by garbling the output of $κ_{2}$. A related partial order stipulates that $κ_{2}$ is more capable than $κ_{1}$ if the mutual information between the input and output is larger for $κ_{2}$ than for $κ_{1}$ for any distribution over inputs. A Blackwell-inferior channel is necessarily less capable. However, examples are known where $κ_{1}$ is less capable than $κ_{2}$ but not Blackwell-inferior. We show that this may even happen when $κ_{1}$ is constructed by coarse-graining the inputs of $κ_{2}$. Such a coarse-graining is a special kind of "pre-garbling" of the channel inputs. This example directly establishes that the expected value of the shared utility function for the coarse-grained channel is larger than it is for the non-coarse-grained channel. This contradicts the intuition that coarse-graining can only destroy information and lead to inferior channels. We also discuss our results in the context of information decompositions.

cs.IT↗

arXiv2017

The thermodynamic efficiency of computations made in cells across the range of life

Biological organisms must perform computation as they grow, reproduce, and evolve. Moreover, ever since Landauer's bound was proposed it has been known that all computation has some thermodynamic cost -- and that the same computation can be achieved with greater or smaller thermodynamic cost depending on how it is implemented. Accordingly an important issue concerning the evolution of life is assessing the thermodynamic efficiency of the computations performed by organisms. This issue is interesting both from the perspective of how close life has come to maximally efficient computation (presumably under the pressure of natural selection), and from the practical perspective of what efficiencies we might hope that engineered biological computers might achieve, especially in comparison with current computational systems. Here we show that the computational efficiency of translation, defined as free energy expended per amino acid operation, outperforms the best supercomputers by several orders of magnitude, and is only about an order of magnitude worse than the Landauer bound. However this efficiency depends strongly on the size and architecture of the cell in question. In particular, we show that the {\it useful} efficiency of an amino acid operation, defined as the bulk energy per amino acid polymerization, decreases for increasing bacterial size and converges to the polymerization cost of the ribosome. This cost of the largest bacteria does not change in cells as we progress through the major evolutionary shifts to both single and multicellular eukaryotes. However, the rates of total computation per unit mass are nonmonotonic in bacteria with increasing cell size, and also change across different biological architectures including the shift from unicellular to multicellular eukaryotes.

q-bio.OT↗

arXiv2017

When is a bit worth much more than kT ln2?

Physical processes thatobtain, process, and erase information involve tradeoffs between information and energy. The fundamental energetic value of a bit of information exchanged with a reservoir at temperature T is kT ln2. This paper investigates the situation in which information is missing about just what physical process is about to take place. The fundamental energetic value of such information can be far greater than kT ln2 per bit.

cond-mat.stat-mech↗

arXiv2017

Modeling Social Organizations as Communication Networks

We identify the "organization" of a human social group as the communication network(s) within that group. We then introduce three theoretical approaches to analyzing what determines the structures of human organizations. All three approaches adopt a group-selection perspective, so that the group's network structure is (approximately) optimal, given the information-processing limitations of agents within the social group, and the exogenous welfare function of the overall group. In the first approach we use a new sub-field of telecommunications theory called network coding, and focus on a welfare function that involves the ability of the organization to convey information among the agents. In the second approach we focus on a scenario where agents within the organization must allocate their future communication resources when the state of the future environment is uncertain. We show how this formulation can be solved with a linear program. In the third approach, we introduce an information synthesis problem in which agents within an organization receive information from various sources and must decide how to transform such information and transmit the results to other agents in the organization. We propose leveraging the computational power of neural networks to solve such problems. These three approaches formalize and synthesize work in fields including anthropology, archeology, economics and psychology that deal with organization structure, theory of the firm, span of control and cognitive limits on communication.

cs.SI↗

arXiv2016

A quantitative definition of organismality and its application to lichen

The organism is a fundamental concept in biology. However there is no universally accepted, formal, and yet broadly applicable definition of what an organism is. Here we introduce a candidate definition. We adopt the view that the "organism" is a functional concept, used by scientists to address particular questions concerning the future state of a biological system, rather than something wholly defined by that system. In this approach organisms are a coarse-graining of a fine-grained dynamical model of a biological system. Crucially, the coarse-graining of the system into organisms is chosen so that their dynamics can be used by scientists to make accurate predictions of those features of the biological system that interests them, and do so with minimal computational burden. To illustrate our framework we apply it to a dynamic model of lichen symbiosis---a system where either the lichen or its constituent fungi and algae could reasonably be considered "organisms." We find that the best choice for what organisms are in this scenario are complex mixtures of many entities that do not resemble standard notions of organisms. When we restrict our allowed coarse-grainings to more traditional types of organisms, we find that ecological conditions, such as niche competition and predation pressure, play a significant role in determining the best choice for organisms.

q-bio.OT↗

arXiv2016

A Likelihood Ratio Detector for Identifying Within-Perimeter Computer Network Attacks

The rapid detection of attackers within firewalls of enterprise computer net- works is of paramount importance. Anomaly detectors address this problem by quantifying deviations from baseline statistical models of normal network behav- ior and signaling an intrusion when the observed data deviates significantly from the baseline model. However, many anomaly detectors do not take into account plausible attacker behavior. As a result, anomaly detectors are prone to a large number of false positives due to unusual but benign activity. This paper first in- troduces a stochastic model of attacker behavior which is motivated by real world attacker traversal. Then, we develop a likelihood ratio detector that compares the probability of observed network behavior under normal conditions against the case when an attacker has possibly compromised a subset of hosts within the network. Since the likelihood ratio detector requires integrating over the time each host be- comes compromised, we illustrate how to use Monte Carlo methods to compute the requisite integral. We then present Receiver Operating Characteristic (ROC) curves for various network parameterizations that show for any rate of true posi- tives, the rate of false positives for the likelihood ratio detector is no higher than that of a simple anomaly detector and is often lower. We conclude by demon- strating the superiority of the proposed likelihood ratio detector when the network topologies and parameterizations are extracted from real-world networks.

cs.CR↗

arXiv2013

Cyber-Physical Security: A Game Theory Model of Humans Interacting over Control Systems

Recent years have seen increased interest in the design and deployment of smart grid devices and control algorithms. Each of these smart communicating devices represents a potential access point for an intruder spurring research into intruder prevention and detection. However, no security measures are complete, and intruding attackers will compromise smart grid devices leading to the attacker and the system operator interacting via the grid and its control systems. The outcome of these machine-mediated human-human interactions will depend on the design of the physical and control systems mediating the interactions. If these outcomes can be predicted via simulation, they can be used as a tool for designing attack-resilient grids and control systems. However, accurate predictions require good models of not just the physical and control systems, but also of the human decision making. In this manuscript, we present an approach to develop such tools, i.e. models of the decisions of the cyber-physical intruder who is attacking the systems and the system operator who is defending it, and demonstrate its usefulness for design.

cs.GT↗

arXiv2011

Using Supervised Learning to Improve Monte Carlo Integral Estimation

Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications in aerospace engineering, the calculation of expected values of such functions (e.g. performance measures) becomes important. However, MC techniques often suffer from high variance and slow convergence as the number of samples increases. In this paper we present Stacked Monte Carlo (StackMC), a new method for post-processing an existing set of MC samples to improve the associated integral estimate. StackMC is based on the supervised learning techniques of fitting functions and cross validation. It should reduce the variance of any type of Monte Carlo integral estimate (simple sampling, importance sampling, quasi-Monte Carlo, MCMC, etc.) without adding bias. We report on an extensive set of experiments confirming that the StackMC estimate of an integral is more accurate than both the associated unprocessed Monte Carlo estimate and an estimate based on a functional fit to the MC samples. These experiments run over a wide variety of integration spaces, numbers of sample points, dimensions, and fitting functions. In particular, we apply StackMC in estimating the expected value of the fuel burn metric of future commercial aircraft and in estimating sonic boom loudness measures. We compare the efficiency of StackMC with that of more standard methods and show that for negligible additional computational cost significant increases in accuracy are gained.

stat.ML↗

arXiv2008

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents' moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of ``semicoordinate'' variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for $k$-sat constraint satisfaction problems and for unconstrained minimization of $NK$ functions.

cs.NE↗

arXiv2008

Bias-Variance Techniques for Monte Carlo Optimization: Cross-validation for the CE Method

In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL algorithms is the bias-variance tradeoff. This tradeoff has been used to improve PL algorithms ranging from Monte Carlo estimation of integrals, to linear estimation, to general statistical estimation. Moreover, as described by, MCO is very closely related to PL. Owing to this similarity, the bias-variance tradeoff affects MCO performance, just as it does PL performance. In this article, we exploit the bias-variance tradeoff to enhance the performance of MCO algorithms. We use the technique of cross-validation, a technique based on the bias-variance tradeoff, to significantly improve the performance of the Cross Entropy (CE) method, which is an MCO algorithm. In previous work we have confirmed that other PL techniques improve the perfomance of other MCO algorithms. We conclude that the many techniques pioneered in PL could be investigated as ways to improve MCO algorithms in general, and the CE method in particular.

math.NA↗

arXiv2008

Bias-Variance Tradeoffs: Novel Applications

We present several applications of the bias-variance decomposition, beginning with straightforward Monte Carlo estimation of integrals, but progressing to the more complex problem of Monte Carlo Optimization (MCO), which involves finding a set of parameters that optimize a parameterized integral. We present the similarity of this application to that of Parametric Learning (PL). Algorithms in this field use a particular interpretation of the bias-variance trade to improve performance. This interpretation also applies to MCO, and should therefore improve performance. We verify that this is indeed the case for a particular MCO problem related to adaptive importance sampling.

stat.AP↗

arXiv2003

Collectives for the Optimal Combination of Imperfect Objects

In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world utility rating the behavior of that overall system that the designer of the collective wishes to optimize. We then apply algorithms based on that work on a recently suggested testbed for such optimization problems (Challet & Johnson, PRL, vol 89, 028701 2002). This is the problem of finding the combination of imperfect nano-scale objects that results in the best aggregate object. We present experimental results showing that these algorithms outperform conventional methods by more than an order of magnitude in this domain.

cond-mat.dis-nn↗

arXiv2003

Improving Search Algorithms by Using Intelligent Coordinates

We consider the problem of designing a set of computational agents so that as they all pursue their self-interests a global function G of the collective system is optimized. Three factors govern the quality of such design. The first relates to conventional exploration-exploitation search algorithms for finding the maxima of such a global function, e.g., simulated annealing. Game-theoretic algorithms instead are related to the second of those factors, and the third is related to techniques from the field of machine learning. Here we demonstrate how to exploit all three factors by modifying the search algorithm's exploration stage so that rather than by random sampling, each coordinate of the underlying search space is controlled by an associated machine-learning-based ``player'' engaged in a non-cooperative game. Experiments demonstrate that this modification improves SA by up to an order of magnitude for bin-packing and for a model of an economic process run over an underlying network. These experiments also reveal novel small worlds phenomena.

math.OC↗