10 December 2018

Data Science: Generalization (Just the Quotes)

"General assertions, like general truths, are not always applicable to individual cases [...]" (Letitia E Landon, "Romance and Reality", 1831)

"Every science begins by accumulating observations, and presently generalizes these empirically; but only when it reaches the stage at which its empirical generalizations are included in a rational generalization does it become developed science." (Herbert Spencer, "The Data of Ethics", 1879)

"Let us notice first of all, that every generalization implies in some measure the belief in the unity and simplicity of nature." (Jules H Poincaré, "Science and Hypothesis", 1905)

"We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features." (Eliakim H Moore, "Introduction to a Form of General Analysis", 1910)

"Sometimes the probability in favor of a generalization is enormous, but the infinite probability of certainty is never reached." (William Dampier-Whetham, "Science and the Human Mind", 1912)

"Generalization is the golden thread which binds many facts into one simple description." (Joseph W Mellor, "A Comprehensive Treatise on Inorganic and Theoretical Chemistry", 1922)

"The former distrust of specialization has been supplanted by its opposite, a distrust of generalization. Not only has man become a specialist in practice, he is being taught that special facts represent the highest form of knowledge." (Richard Weaver, "Ideas have Consequences", 1948)

"The transition from a paradigm to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field’s most elementary theoretical generalizations as well as many of its paradigm methods and applications." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"Theories are generalizations and unifications, and as such they cannot logically follow only from our experiences of a few particular events." (John T Davies, The Scientific Approach, 1965)

"At each level of complexity, entirely new properties appear. [And] at each stage, entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one." (Herb Anderson, 1972)

"Science uses the senses but does not enjoy them; finally buries them under theory, abstraction, mathematical generalization." (Theodore Roszak, "Where the Wasteland Ends", 1972)

"Almost all efforts at data analysis seek, at some point, to generalize the results and extend the reach of the conclusions beyond a particular set of data. The inferential leap may be from past experiences to future ones, from a sample of a population to the whole population, or from a narrow range of a variable to a wider range. The real difficulty is in deciding when the extrapolation beyond the range of the variables is warranted and when it is merely naive. As usual, it is largely a matter of substantive judgment - or, as it is sometimes more delicately put, a matter of 'a priori nonstatistical considerations'." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"A single observation that is inconsistent with some generalization points to the falsehood of the generalization, and thereby 'points to itself'." (Ian Hacking, "The Emergence Of Probability", 1975)

"The word generalization in literature usually means covering too much territory too thinly to be persuasive, let alone convincing. In science, however, a generalization means a principle that has been found to hold true in every special case." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)

"Prediction can never be absolutely valid and therefore science can never prove some generalization or even test a single descriptive statement and in that way arrive at final truth." (Gregory Bateson, "Mind and Nature, A necessary unity", 1979)

"There are those who try to generalize, synthesize, and build models, and there are those who believe nothing and constantly call for more data. The tension between these two groups is a healthy one; science develops mainly because of the model builders, yet they need the second group to keep them honest." (Andrew Miall, "Principles of Sedimentary Basin Analysis", 1984)

"We generalize from one situation to another not because we cannot tell the difference between the two situations but because we judge that they are likely to belong to a set of situations having the same consequence." (Roger N Shepard, "Toward a Universal Law of Generalization for Psychological Science", Science 237 (4820), 1987)

"Searching for patterns is a way of thinking that is essential for making generalizations, seeing relationships, and understanding the logic and order of mathematics. Functions evolve from the investigation of patterns and unify the various aspects of mathematics." (Marilyn Burns, "About Teaching Mathematics: A K–8 Resource", 1992)

"Generalization is the process of matching new, unknown input data with the problem knowledge in order to obtain the best possible solution, or one close to it. Generalization means reacting properly to new situations, for example, recognizing new images, or classifying new objects and situations. Generalization can also be described as a transition from a particular object description to a general concept description. This is a major characteristic of all intelligent systems." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"Generalization is a core concept in machine learning; to be useful, machine-learning algorithms can’t just memorize the past, they must learn from the past. Generalization is the ability to respond properly to new situations based on experience from past situations." (Prashant Natarajan et al, "Demystifying Big Data and Machine Learning for Healthcare", 2017)

"In machine learning, a model is defined as a function, and we describe the learning function from the training data as inductive learning. Generalization refers to how well the concepts are learned by the model by applying them to data not seen before. The goal of a good machine-learning model is to reduce generalization errors and thus make good predictions on data that the model has never seen." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)

"But law is no explanation of anything; law is simply a generalization, a category of facts. Law is neither a cause, nor a reason, nor a power, nor a coercive force. It is nothing but a general formula, a statistical table." (Florence Nightingale)

"Facts are facts and it is from facts that we make our generalizations, from the little to the great, and it is wrong for a stranger to the facts he handles to generalize from them to other generalizations." (Charles Schuchert)

"Generalization is necessary to the advancement of knowledge; but particularity is indispensable to the creations of the imagination." (Thomas B Macaulay)

"Generalizations would be excellent things if we could be persuaded to part with them as easily as we formed them. They might then be used like the shifting hypotheses in certain operations of exact science, by help of which we may gradually approximate nearer and nearer to the truth." (Henry De la Beche)

"No one sees further into a generalization than his own knowledge of detail extends." (William James)

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