McKay's approximation for the coefficient of variation

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BuyRentSingaporeProperty.com is dedicated in providing the newest residential launches, Developer's sales, new launches, resale, HIGH tasks and rental of properties in Singapore. Then there are new launch property condos in the mid-tier range. These are sometimes in the vicinity of the city fringe, in areas corresponding to Newton and Novena Tanjong Rhu. These new launch projects are popular due to their proximity to town heart, the place the enterprise and entertainment centers and all the amenities they provide, but they're usually cheaper than the City core region tasks. Why submit cheques to register for new property launches in Singapore? Riversails Apartment @ Higher Serangoon LakeVille @ Jurong Lakeside Condo by MCL Ferra Condo @ Leonie Hill In machine learning, the bias-variance dilemma or bias-variance tradeoff is the problem of simultaneously minimizing the bias (how accurate a model is across different training sets) and variance of the model error (how sensitive the model is to small changes in training set). This tradeoff applies to all forms of supervised learning: classification, function fitting,[1][2] and structured output learning.

The bias-variance tradeoff is a central problem in supervised learning. Intuitively, it means that a model must be chosen that at the same time captures the regularities in its training data, but also generalizes well to unseen data. Models can have high bias, meaning they impose restrictions on the kind of regularities that can be learned (examples include linear classifiers), or they can have high variance, meaning they can learn many kinds of complex regularities—including noise in the training data (e.g., very deep decision trees). To achieve good performance on data outside the training set, a tradeoff must be made.

Relevance

This trade-off is related to issues of overfitting and underfitting. Models that reliably have small deviations from the training set are typically bad predictors for non-training set inputs and will change significantly if the set changes (making them sensitive to outliers and noise). Meanwhile models that systematically deviate can resist noise and generalise well, although too strong deviation decreases performance.

Typically the goal is to find an optimal trade-off between bias and variance. A common model selection criterion is that the decrease of bias with increasing model complexity becomes equal to the increase of variance. There are however other possible considerations, such as error losses or complexity costs, that may lead to other trade-offs. The choice of model may also introduce biases that correspond to useful prior information, for example that the output must be within a given interval.

Bias-Variance decomposition

(After [3])

Suppose we have data derived from the true model , where is a random variable with .

Given the data, we train a model to approximate . For brevity and clarity will be written as below. Similarly .

The mean-squared error is .

The value of interest is the expectation of the MSE across different realisations of data:

This formula can be split apart:

Now, since f is deterministic and , , and . Hence the last term above sums to zero:

The second term can be decomposed in the same way using the same trick:

Hence

The expected MSE is hence composed of an irreducible error due to the noise (the first term), a bias due to the model systematically deviating from f (the second term), and a variance due to the model not perfectly predicting the particular realization of the data (the third term).

In the above the data was written as scalar values, but the decomposition works for vectorial data too.

Approaches

Cross-validation is widely used to check model error by testing on data not part of the training set. Multiple rounds with randomly selected test sets are averaged together to reduce variability of the cross-validation; high variability of the model will produce high average errors on the test set.

One way of resolving the trade-off is to use mixture models and ensemble learning.[4][5] For example, boosting combines many "weak" (high bias) models in an ensemble that has greater variance than the individual models, while bagging combines "strong" learners in a way that reduces their variance.

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

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    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  2. Bias-Value decomposition, In Encyclopedia of Machine Learning. Eds. Claude Sammut, Geoffrey I. Webb. Springer 2011. pp. 100-101
  3. Sethu Vijayakumar. The Bias-Variance Tradeoff. Lecture notes, University Edinburgh 2007. http://www.inf.ed.ac.uk/teaching/courses/mlsc/Notes/Lecture4/BiasVariance.pdf
  4. Jo-Anne Ting, Sethu Vijaykumar, Stefan Schaal, Locally Weighted Regression for Control. In Encyclopedia of Machine Learning. Eds. Claude Sammut, Geoffrey I. Webb. Springer 2011. p. 615
  5. Scott Fortmann-Roe. Understanding the Bias-Variance Tradeoff. 2012. http://scott.fortmann-roe.com/docs/BiasVariance.html