Using statistical methods to model the fine-tuning of molecular machines and systems

Thorvaldsen, Steinar; Hössjer, Ola

doi:10.1016/j.jtbi.2020.110352

Cited by 16 publications

(12 citation statements)

References 59 publications

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“…The population of bacteria learns S at time k if there is a phase transition such that up to (G k−1 , D k−1 ) the probability of the population acting as a unit is null, whereas it becomes positive for (G k , D k ). This is closely related to fine-tuning of biological systems Thorvaldsen & Hössjer, 2020). As for the direction of causation from cognition to code, Kolmogorov's complexity, which measures the complexity of an outcome as the shortest code that produces it, can be used in place of or jointly with active information to measure learning (Ewert et al, 2015).…”

Section: Discussionmentioning

confidence: 99%

“…According to Definition 1, the upper part of (15) represents a maximum amount of learning, that is, P(A) = 1; whereas the lower part corresponds to a maximal amount of false belief about S when x 0 ∈ A, that is, P(A) = 0 (see also . Suppose S is a proposition that a certain entity or machine functions, then − log P 0 (A) is the functional information associated with the event A of observing such functioning entity Szostak, 2003;Thorvaldsen & Hössjer, 2020). Consequently, in our context, functional information corresponds to the maximal amount of learning about S when the machine works ( f (x 0 ) = 1).…”

Section: Active Information Learning and Knowledgementioning

confidence: 99%

See 1 more Smart Citation

A Formal Framework for Knowledge Acquisition: Going Beyond Machine Learning

Hössjer¹,

Díaz–Pachón²,

Rao³

2021

Preprint

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Philosophers frequently define knowledge as justified, true belief. In this paper we build a mathematical framework that makes possible to define learning (increased degree of true belief) and knowledge of an agent in precise ways. This is achieved by phrasing belief in terms of epistemic probabilities, defined from Bayes' Rule. The degree of true belief is then quantified by means of active information $I^+$, that is, a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent's strength of belief in a true proposition has increased in comparison with the ignorant person ($I^+>0$), or if the strength of belief in a false proposition has decreased ($I^+<0$). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds, of which one is true and the others are counterfactuals. We also generalize the framework of learning and knowledge acquisition to a sequential setting, where information and data is updated over time. The theory is illustrated using examples of coin tossing, historical events, future events, replication of studies, and causal inference.

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Section: Discussionmentioning

confidence: 99%

Section: Active Information Learning and Knowledgementioning

confidence: 99%

A Formal Framework for Knowledge Acquisition: Going Beyond Machine Learning

Hössjer¹,

Díaz–Pachón²,

Rao³

2021

Preprint

Self Cite

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“…Through this lens, a crucial part of the analysis of tuning is mathematical modeling, and cosmological fine-tuning is one particular instantiation. Every mathematical model, whether developed for theoretical or applied purposes, will require parameters, and those parameters can always be analyzed from a fine-tuning perspective [48,49].…”

Section: Determining the Constraintsmentioning

confidence: 99%

Sometimes size does not matter

Díaz–Pachón¹,

Hössjer²,

Marks³

2022

Preprint

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Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the interval, not on its size. Most attempts to measure the probability of the life-permitting interval for a given parameter rely on a Bayesian statistical approach for which the prior distribution of the parameter is uniform. However, the parameters in these models often take values in spaces of infinite size, so that a uniformity assumption is not possible. This is known as the normalization problem. This paper explains a framework to measure tuning that, among others, deals with normalization, assuming that the prior distribution belongs to a class of maximum entropy (maxent) distributions. By analyzing an upper bound of the tuning probability for this class of distributions the method solves the so-called weak anthropic principle, and offer a solution, at least in this context, to the well-known lack of invariance of maxent distributions. The implication of this approach is that, since all mathematical models need parameters, tuning is not only a question of natural science, but also a problem of mathematical modeling. Cosmological tuning is thus a particular instantiation of a more general scenario. Therefore, whenever a mathematical model is used to describe nature, not only in physics but Size does not matter in all of science, tuning is present. And the question of whether the tuning is fine or coarse for a given parameter -if the interval in which the parameter is located has low or high probability, respectively -depends crucially not only on the interval but also on the assumed class of prior distributions. Novel upper bounds for tuning probabilities are presented.

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“…The paper [37] uses the traditional clustering model as the teacher model. Moreover, the teacher model T is also called the pre-trained model in the fine-tuning method [44]. However, unlike the fine-tuning method, we try to learn knowledge from the pretrained model instead of adjusting it.…”

Section: Guided Learningmentioning

confidence: 99%