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[1805.07360] Prediction in Projection: A new paradigm in delay-coordinate reconstruction
Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the associated theory and heuristics are overly stringent for real-world data, however, and real-time use is out of the question due to the expert human intuition needed to use these heuristics correctly. The approach outlined in this thesis represents a paradigm shift away from that traditional approach. I argue that perfect reconstructions are not only unnecessary for the purposes of delay-coordinate based forecasting, but that they can often be less effective than reduced-order versions of those same models. I demonstrate this using a range of low- and high-dimensional dynamical systems, showing that forecast models that employ imperfect reconstructions of the dynamics---i.e., models that are not necessarily true embeddings---can produce surprisingly accurate predictions of the future state of these systems. I develop a theoretical framework for understanding why this is so. This framework, which combines information theory and computational topology, also allows one to quantify the amount of predictive structure in a given time series, and even to choose which forecast method will be the most effective for those data.
nonlinear-dynamics  representation  complexology  rather-interesting  to-write-about  to-understand 
3 days ago by Vaguery
Symmathesy: A Word in Progress | norabateson
I would like to propose a new word for “System” that refers specifically to living systems – that is, to systems which emerge from the communications and interactions of living vitae (another new term, one which will be defined later). The new word, and concept, for “system” that I propose is one which highlights the expression and communication of interdependency and, particularly, mutual learning. The existing word, “system”, while useful for discussion of many kinds of systems, does not communicate contextual fields of simultaneous learning as is necessary for life. The inclusion of mutual learning in the terminology is specifically meant to preclude the models of engineering and mechanism that are implicit in much systems theorizing today.   We have learned that when dealing with living systems, the many variables of developing interaction become untenable to consider in such mechanistic parameters. This change in concept should spark a significant shift in our work, in the sciences, applied professions, communication, arts, that addresses or depends upon our understanding of life and evolution. The discourse with which we discuss and study the living world should be representative of the living world, and should cautiously avoid connotations that imply or are derived from engineering.

The notion of systems as being an arrangement of parts and wholes has become a distraction from the new systemic vision, which we are trying to encourage, that sees life as relational mutual learning contexts. As studies ranging from cognitive science to epigenetics, social science, ecology and evolutionary theory, are increasingly showing, evolution emerges in interrelationality, not in arrangement. Therefore the need is acute to create a differentiation between living systems and other systems.
complexology  representation  define-your-terms  rather-interesting  to-write-about  philosophy-of-science 
3 days ago by Vaguery
Kumaraswamy distribution: a beta-like probability density
Maybe the algorithm I suggested for picking parameters is not very good, but I suspect the optimal parameters are not much better. Rather than saying that the Kumaraswamy distribution approximates the beta distribution, I’d say that the Kumaraswamy distribution is capable of assuming roughly the same shapes as the beta distribution. If the only reason you’re using a beta distribution is to get a certain density shape, the Kumaraswamy distribution would be a reasonable alternative. But if you need to approximate a beta distribution closely, it may not work well enough.
probability-theory  representation  rather-interesting  to-write-about  consider:feature-discovery  consider:heuristics  consider:approximation 
3 days ago by Vaguery
[1805.11813] Derivatives of Turing machines in Linear Logic
We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally arising in the Sweedler semantics of linear logic proofs. The resulting theory is applied to the problem of synthesising Turing machines by gradient descent.
computer-science  representation  to-understand  rather-interesting 
3 days ago by Vaguery
[1805.10872] DeepProbLog: Neural Probabilistic Logic Programming
We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments demonstrate that DeepProbLog supports both symbolic and subsymbolic representations and inference, 1) program induction, 2) probabilistic (logic) programming, and 3) (deep) learning from examples. To the best of our knowledge, this work is the first to propose a framework where general-purpose neural networks and expressive probabilistic-logical modeling and reasoning are integrated in a way that exploits the full expressiveness and strengths of both worlds and can be trained end-to-end based on examples.
deep-learning  representation  probabilistic-programming  rather-interesting  to-understand 
10 days ago by Vaguery
[1806.02717] Gamorithm
Examining games from a fresh perspective we present the idea of game-inspired and game-based algorithms, dubbed "gamorithms".
hey-I-know-this-guy  machine-learning  philosophy-of-engineering  representation  to-write-about 
10 days ago by Vaguery
[1805.12244] Mining gold from implicit models to improve likelihood-free inference
Simulators often provide the best description of real-world phenomena; however, they also lead to challenging inverse problems because the density they implicitly define is often intractable. We present a new suite of simulation-based inference techniques that go beyond the traditional Approximate Bayesian Computation approach, which struggles in a high-dimensional setting, and extend methods that use surrogate models based on neural networks. We show that additional information, such as the joint likelihood ratio and the joint score, can often be extracted from simulators and used to augment the training data for these surrogate models. Finally, we demonstrate that these new techniques are more sample efficient and provide higher-fidelity inference than traditional methods.
machine-learning  simulation  representation  randomness  to-understand  to-write-about 
10 days ago by Vaguery
[1805.09460] Cautious Deep Learning
Most classifiers operate by selecting the maximum of an estimate of the conditional distribution p(y|x) where x stands for the features of the instance to be classified and y denotes its label. This often results in a hubristic bias: overconfidence in the assignment of a definite label. Usually, the observations are concentrated on a small volume but the classifier provides definite predictions for the entire space. We propose constructing conformal prediction sets [vovk2005algorithmic] which contain a set of labels rather than a single label. These conformal prediction sets contain the true label with probability 1−α. Our construction is based on p(x|y) rather than p(y|x) which results in a classifier that is very cautious: it outputs the null set - meaning `I don't know' --- when the object does not resemble the training examples. An important property of our approach is that classes can be added or removed without having to retrain the classifier. We demonstrate the performance on the ImageNet ILSVRC dataset using high dimensional features obtained from state of the art convolutional neural networks.
define-your-terms  representation  rather-interesting  machine-learning  conservative-estimates  performance-measure  to-write-about 
10 days ago by Vaguery
[1803.06824] Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. Since a finite volume of space can't contain more than a finite amount of information, I argue that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is "random numbers", as their series of bits are truly random. I propose an alternative classical mechanics, which is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. I argue that it is more economical and natural to accept non-determinism with potentialities as a real mode of existence, both for classical and quantum physics.
philosophy-of-science  mathematics  representation  rather-interesting  to-understand  information-theory  huh 
10 days ago by Vaguery

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