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Foundations of Genomic Signal Processing The Mathematical Basis of Biological Knowledge: Epistemology of Computational

9/22/2012. gsp.tamu.edu. The Epistemological Problem. Systems biology, and genomics in particular, raises the epistemological problem. The role played by stochastic nonlinear dynamical systems precludes an uncritical reductionist realism.Genomics eliminates the possibility of an uncritical underst

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Foundations of Genomic Signal Processing The Mathematical Basis of Biological Knowledge: Epistemology of Computational

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    1. 9/22/2012 gsp.tamu.edu Foundations of Genomic Signal Processing *************************************************** The Mathematical Basis of Biological Knowledge: Epistemology of Computational Biology Edward R. Dougherty Department of Electrical and Computer Engineering, Texas A&M University Computational Biology Division, Translational Genomics Research Institute

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    5. 9/22/2012 gsp.tamu.edu Classification Looks Promising It looks like gene expression can be used to diagnose hereditary breast cancers.

    6. 9/22/2012 gsp.tamu.edu What Does This Mean? The sample data are perfectly separated, but is there scientific knowledge?

    7. 9/22/2012 gsp.tamu.edu The Clustering Oxymoron Error rate: 16.6% Picture looks good. Unsupervised learning is an oxymoron. Science?

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    14. 9/22/2012 gsp.tamu.edu Scientific Experiment Hans Reichenbach (The Rise of Scientific Philosophy): As long as we depend on the observation of occurrences not involving our assistance, the observable happenings are usually the product of so many factors that we cannot determine the contribution of each individual factor to the total result. The scientific experiment isolates the factors from each other; the interference of man creates conditions in which one factor is shown at work undisturbed by the others. Scientific experimentation is not mere observation; it is methodological observation.

    15. 9/22/2012 gsp.tamu.edu From Reasoning to Science Hans Reichenbach: By means of the artificial occurrences of planned experiments, the complex occurrence of Nature is thus analyzed into its components. That Greek science did not use experiments in any significant way proves how difficult it was to turn from reasoning to empirical science. Science is not constituted by reasoning about data; it is constituted by pragmatic, predictive models.

    16. 9/22/2012 gsp.tamu.edu Secure Path of Science Immanuel Kant (Critique of Pure Reason, 1786): Reason has insight only into that which it produces after a plan of its own, constraining Nature to give answer to questions of reasons own determining Reason must approach Nature [as] an appointed judge who compels the witness to answer questions which he himself has formulated It is thus that the study of Nature has entered on the secure path of science after having for so long many centuries been nothing but a process of merely random groping.

    17. 9/22/2012 gsp.tamu.edu The Decisive Point William Barrett: [For Galileo] it was necessary to have a clear-cut concept of inertia as a fundamental characteristic of moving bodies... He sets up a concept that could never be realized in actual fact... Reason becomes legislative of experience this was the decisive point that Kants genius perceived as the real revolution of the new science. William Barrett: The scientist constructs models, which are not found among the things given him in his experience, and proceeds to impose those models upon Nature.

    18. Scientific Amnesia John Potter: Making the observations with new and powerful technology seems to induce amnesia as to the original nature of the study design. It is though astronomers were to ignore every thing they knew both about how to classify stars and about sampling methods, and instead were to point spectroscopes haphazardly at stars and note how different and interesting the pattern of spectral absorption lines were... This dilettantes approach to either astronomy or biology has not been in vogue for at least half a century. Potter, J. D. At the Interfaces of Epidemiology, Genetics and Genomics. Nature Reviews/Genetics, 2, 142-147, 2001.

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    20. 9/22/2012 gsp.tamu.edu Richard Feynman: The laws are guessed; they are extrapolations into the unknown. Albert Einstein: Experience, of course, remains the sole criterion for the serviceability of mathematical constructions for physics, but the truly creative principle resides in mathematics. The veracity of a scientific model lies in experience, but its conception arises from the imagination. Scientific Discovery is Imaginative

    21. 9/22/2012 gsp.tamu.edu Mathematics Carries Scientific Knowledge James Jeans: The final truth about phenomena resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge is complete. We go beyond the mathematical formula at our own risk; we may find a [nonmathematical] model or picture which helps us to understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. Absent an understanding of the mathematics behind an analysis, there is no scientific understanding.

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    23. 9/22/2012 gsp.tamu.edu Richard Feynman: It is whether or not the theory gives predictions that agree with experiment. It is not a question of whether a theory is philosophically delightful, or easy to understand, or perfectly reasonable from the point of view of common sense. The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is absurd. Nature Is Absurd

    24. We understand the mathematical model because it is a product of human intelligence. We do not understand Nature, nor should we expect to. Implicit in Feynmans comment is the existence of a set of statements whose predictive capability can be experimentally examined independent of reason. Mental pictures are a step away from reality (Jeans) because they are not predictive. Descartes: Clear and distinct ideas guarantee truth. We Understand Mathematics, Not Nature

    25. Hans Reichenbach: If the abstract relations are general truths, they hold not only for the observations made, but also for observations not yet made; they include not only an account of past experiences, but also predictions of future experiences. That is the addition which reason makes to knowledge. Observation informs us about the past and the present, reason foretells the future. Reason produces the components required for prediction: experiment, model, operational definitions Role of Reason

    26. 9/22/2012 gsp.tamu.edu Hans Reichenbach: The new empiricism may be called a functional conception of knowledge Knowledgeportrays the things of this world so as to serve a function serving a purpose, the purpose of predicting the future. Richard Feynman: Knowledge is of no real value if all you can tell me is what happened yesterday. Scientific knowledge is not the collection of facts and explanation them by an a posteriori model. Scientific Knowledge is Functional

    27. 9/22/2012 gsp.tamu.edu Scientific Knowledge is Methodological William James: Truth happens to an idea. It becomes true, is made true by events. Its verity is in fact an event, a process, the process namely of its verifying itself, its verification. Its validity is the process of its validation. Scientific knowledge does not lie with an image in the mind agreeing with a phenomenon (Aristotle); rather, it lies in adherence to a method (process).

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    29. 9/22/2012 gsp.tamu.edu Science is Inter-subjective Karl Popper: The objectivity of scientific statements lies in the fact that they can be inter-subjectively tested. Inter-subjectivity demands that scientific knowledge not depend on reason, except within the strict rules of mathematics; otherwise, philosophical theories like Marxism could legitimately claim to be science. This would be cult science, open only to those who claim to understand empty phrases such as dialectical materialism.

    30. 9/22/2012 gsp.tamu.edu Science Requires Observability Erwin Schrodinger: It really is the ultimate purpose of all schemes and models to serve as scaffolding for any observations that are at all conceivable There does not seem to be much sense in inquiring about the real existence of something, if one is convinced that the effect through which the thing would manifest itself, in case it existed, is certainly not observable. Without observable effects due to an object, the object is not a subject of scientific inquiry.

    31. 9/22/2012 gsp.tamu.edu Scientific Meaning Lies in Verifiability Hans Reichenbach: The reference to verifiability is a necessary constituent of the theory of meaning. A sentence the truth of which cannot be determined from possible observations is meaningless. We are back to William James: The validity of a statement is the process of its validation.

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    33. 9/22/2012 gsp.tamu.edu The Meaning of Validity is Mathematical There is no nonmathematical way to precisely describe knowledge regarding model validity. It depends on the choice of validity measurement and the mathematical properties of that measurement as applied in different circumstances. In all cases, the nature of our knowledge rests with the mathematical theory we have concerning the measurements. That cannot be simplified. If either the available theory or ones familiarity with the theory is limited, then ones appreciation of the scientific content of a model is limited. Dougherty, E. R., Hua, J., and M. L. Bittner, Validation of Computational Methods in Genomics, Current Genomics, 8 (1), 1-19, 2007..

    34. 9/22/2012 gsp.tamu.edu Science is not Explanatory William Dembski: Admitting [intelligent] design into science can only enrich the scientific enterprise. All the tried and true tools of science will remain intact. But design adds a new tool to the scientists explanatory tool chest. The problem here is that the scientist has no explanatory tool chest. The scientist has a method. Dembski has given us no mathematical model, no operational definitions, and no experimental protocol.

    35. 9/22/2012 gsp.tamu.edu Scientific Knowledge is Contingent Karl Popper: [The scientific method's] aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival. A model is accepted so long as no new experiment invalidates its predictions. Science does not concern eternal truth.

    36. 9/22/2012 gsp.tamu.edu A Scientific Theory is Falsifiable Karl Popper: Insofar as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality. For an assertion to be falsifiable it must be possible to make an observation or do a physical experiment that would show the assertion to be false. Falsifiability is a minimal necessary condition. Determinism is not falsifiable.

    37. 9/22/2012 gsp.tamu.edu Causality is not a Scientific Category Erwin Schrodinger: It can never be decided experimentally whether causality in nature is 'true' or 'untrue.' The relation of cause and effect, as Hume pointed out long ago, is not something that we find in Nature but is rather a characteristic of the way in which we regard Nature. Hans Reichenbach: The happenings of Nature are like rolling dice rather than revolving stars; they are controlled by probability laws, not causality, and the scientist resembles a gambler rather than a prophet.

    38. 9/22/2012 gsp.tamu.edu Probability Theory is the Logic of Science Hans Reichenbach: The theory of probability supplies the instrument of predictive knowledge as well as the form of the laws of nature: its subject is the very nerve of scientific method. Even if the real world were deterministic, we would not be able to capture the determinism because all models are partial, thereby suffering from latent variables, and all measurements have error. Since scientific knowledge is based on prediction, there is no possibility for it to be other than probabilistic.

    39. 9/22/2012 gsp.tamu.edu Ground of Genomic Signal Processing Classification: Operators on jointly distributed random variables to label a random vector. Clustering: Operators on random point sets to partition a point set. Networks: Operators on vector random processes to alter the dynamics of a random process.

    40. 9/22/2012 gsp.tamu.edu What Does This Mean? As it stands, it is the product of an algorithm scientifically meaningless. It becomes scientifically meaningful if there is a precise experimental protocol under which it predicts outcomes. This requires an error rate so model validity relates to the accuracy of error estimation.

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