lower-bounds   50

Applications of computational learning theory in the cognitive sciences - Psychology & Neuroscience Stack Exchange
1. Gold's theorem on the unlearnability in the limit of certain sets of languages, among them context-free ones.

2. Ronald de Wolf's master's thesis on the impossibility to PAC-learn context-free languages.

The first made quiet a stir in the poverty-of-the-stimulus debate, and the second has been unnoticed by cognitive science.
q-n-a  stackex  psychology  cog-psych  learning  learning-theory  machine-learning  PAC  lower-bounds  no-go  language  linguistics  models  fall-2015 
28 days ago by nhaliday
[1805.04625] Strong Converse using Change of Measure Arguments
The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we develop a general and simple recipe for proving strong converse that is applicable for distributed problems as well. Heuristically, our proof of strong converse mimics the standard steps for proving a weak converse, except that we apply those steps to a modified distribution obtained by conditioning the original distribution on the event that no error occurs. A key component of our recipe is the replacement of the hard Markov constraints implied by the distributed nature of the problem with a soft information cost using a variational formula introduced by Oohama. We illustrate our method by providing a short proof of the strong converse for the Wyner-Ziv problem and new strong converse theorems for interactive function computation, common randomness and secret key agreement, and the wiretap channel.
papers  to-read  heard-the-talk  information-theory  lower-bounds 
july 2018 by mraginsky
Complexity no Bar to AI - Gwern.net
Critics of AI risk suggest diminishing returns to computing (formalized asymptotically) means AI will be weak; this argument relies on a large number of questionable premises and ignoring additional resources, constant factors, and nonlinear returns to small intelligence advantages, and is highly unlikely. (computer science, transhumanism, AI, R)
created: 1 June 2014; modified: 01 Feb 2018; status: finished; confidence: likely; importance: 10
ratty  gwern  analysis  faq  ai  risk  speedometer  intelligence  futurism  cs  computation  complexity  tcs  linear-algebra  nonlinearity  convexity-curvature  average-case  adversarial  article  time-complexity  singularity  iteration-recursion  magnitude  multiplicative  lower-bounds  no-go  performance  hardware  humanity  psychology  cog-psych  psychometrics  iq  distribution  moments  complement-substitute  hanson  ems  enhancement  parable  detail-architecture  universalism-particularism  neuro  ai-control  environment  climate-change  threat-modeling  security  theory-practice  hacker  academia  realness  crypto  rigorous-crypto  usa  government 
april 2018 by nhaliday
Correlated Equilibria in Game Theory | Azimuth
Given this, it’s not surprising that Nash equilibria can be hard to find. Last September a paper came out making this precise, in a strong way:

• Yakov Babichenko and Aviad Rubinstein, Communication complexity of approximate Nash equilibria.

The authors show there’s no guaranteed method for players to find even an approximate Nash equilibrium unless they tell each other almost everything about their preferences. This makes finding the Nash equilibrium prohibitively difficult to find when there are lots of players… in general. There are particular games where it’s not difficult, and that makes these games important: for example, if you’re trying to run a government well. (A laughable notion these days, but still one can hope.)

Klarreich’s article in Quanta gives a nice readable account of this work and also a more practical alternative to the concept of Nash equilibrium. It’s called a ‘correlated equilibrium’, and it was invented by the mathematician Robert Aumann in 1974. You can see an attempt to define it here:
baez  org:bleg  nibble  mathtariat  commentary  summary  news  org:mag  org:sci  popsci  equilibrium  GT-101  game-theory  acm  conceptual-vocab  concept  definition  thinking  signaling  coordination  tcs  complexity  communication-complexity  lower-bounds  no-go  liner-notes  big-surf  papers  research  algorithmic-econ  volo-avolo 
july 2017 by nhaliday
Predicting the outcomes of organic reactions via machine learning: are current descriptors sufficient? | Scientific Reports
As machine learning/artificial intelligence algorithms are defeating chess masters and, most recently, GO champions, there is interest – and hope – that they will prove equally useful in assisting chemists in predicting outcomes of organic reactions. This paper demonstrates, however, that the applicability of machine learning to the problems of chemical reactivity over diverse types of chemistries remains limited – in particular, with the currently available chemical descriptors, fundamental mathematical theorems impose upper bounds on the accuracy with which raction yields and times can be predicted. Improving the performance of machine-learning methods calls for the development of fundamentally new chemical descriptors.
study  org:nat  papers  machine-learning  chemistry  measurement  volo-avolo  lower-bounds  analysis  realness  speedometer  nibble  🔬  applications  frontier  state-of-art  no-go  accuracy  interdisciplinary 
july 2017 by nhaliday
Energy of Seawater Desalination
0.66 kcal / liter is the minimum energy required to desalination of one liter of seawater, regardless of the technology applied to the process.
infrastructure  explanation  physics  thermo  objektbuch  data  lower-bounds  chemistry  the-world-is-just-atoms  geoengineering  phys-energy  nibble  oceans  h2o  applications  estimate  🔬  energy-resources  biophysical-econ  stylized-facts  ideas  fluid  volo-avolo 
february 2017 by nhaliday

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