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### Prediction and Dimension [chapter]

Lance Fortnow, Jack H. Lutz
2002 Lecture Notes in Computer Science
Our main theorem states that the feasible dimension of X is bounded above by the maximum entropy of the predictability of X and bounded below by the segmented self-information of the predictability of  ...  Predictability is known to be stable in the sense that the feasible predictability of X ∪ Y is always the minimum of the feasible predictabilities of X and Y.  ...  Acknowledgements We thank John Hitchcock, Anumodh Abey, and three anonymous referees for useful suggestions.  ...

### Prediction and dimension

Lance Fortnow, Jack H. Lutz
2005 Journal of computer and system sciences (Print)
Our main theorem states that the feasible dimension of X is bounded above by the maximum entropy of the predictability of X and bounded below by the segmented self-information of the predictability of  ...  Predictability is known to be stable in the sense that the feasible predictability of X ∪ Y is always the minimum of the feasible predictabilities of X and Y.  ...  Acknowledgements We thank John Hitchcock, Anumodh Abey, and three anonymous referees for useful suggestions.  ...

### Statistical Prediction [chapter]

2007 Inference and Prediction in Large Dimensions
V LINEAR PROCESSES IN HIGH DIMENSIONS 215 3.6 Rate in uniform norm . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.7 Adaptive projection . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.7.1  ...  by kernel . . . . . . . . . . . . . . . . . 148 6.5.1 Prediction for a stationary Markov process of order k . . . . 148 6.5.2 Prediction for general processes . . . . . . . . . . . . . . . 150 Functional  ...

### Bibliography [chapter]

2007 Inference and Prediction in Large Dimensions
Inference and Prediction in Large Dimensions D. Bosq and D. Blanke  ...  Chapman and Hall, Boca Raton. Cheze-Payaud N 1994 Nonparametric regression and prediction for continuous time processes. Publ. Inst. Stat. Univ. Paris 38, 37-58.  ...  Bosq D 1991 Modelization, nonparametric estimation and prediction for continuous time processes. In Nonparametric functional estimation and related topics (ed. Roussas) vol. 335 of NATO Adv. Sci.  ...

### Predictive Quantile Regression with Mixed Roots and Increasing Dimensions: ALQR Approach [article]

Rui Fan, Ji Hyung Lee, Youngki Shin
2022 arXiv   pre-print
We apply the proposed method to the out-of-sample quantile prediction problem of stock returns and find that it outperforms the existing alternatives.  ...  In this paper we propose the adaptive lasso for predictive quantile regression (ALQR).  ...  Define a p c -dimensional vector v c t := (v c 1t , v c 2t ) and a p-dimensional vector e t := (z t , v c t , v t ) .  ...

### Clustering and Prediction with Variable Dimension Covariates [article]

Garritt L. Page, Fernando A. Quintana, Peter Müller
2020 arXiv   pre-print
The method we develop allows in-sample predictions as well as out-of-sample prediction, even if the missing pattern in the new subjects' incomplete covariate vector was not seen in the training data.  ...  It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood.  ...  The result is an elegant and uncomplicated variable-dimension regression approach.  ...

### Nearly maximally predictive features and their dimensions

Sarah E. Marzen, James P. Crutchfield
2017 Physical review. E
In such cases, one compromises and instead seeks nearly maximally predictive features.  ...  Here, we derive upper-bounds on the rates at which the number and the coding cost of nearly maximally predictive features scales with desired predictive power.  ...  Supplementary Materials for Nearly Maximally Predictive Features and Their Dimensions Sarah E. Marzen and James P.  ...

### Sufficient dimension reduction and prediction in regression

K. P. Adragni, R. D. Cook
2009 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
The action of replacing X with a lower-dimensional function R(X) is called dimension reduction; it is called sufficient dimension reduction when R(X) retains all the relevant information about Y .  ...  Moment-based sufficient dimension-reduction methods provide estimates of the minimal sufficient linear reduction, but they are not designed specifically for prediction and do not produce predictive methods  ...  Predictions in regression with large p  ...

### Clustering and Prediction With Variable Dimension Covariates

Garritt L. Page, Fernando A. Quintana, Peter Müller
2021 figshare.com
It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood.  ...  The method we develop allows in-sample as well as out-of-sample predictions, even if the missing pattern in the new subjects' incomplete covariate vector was not seen in the training data.  ...  In terms of prediction, BART and VDReg are the only procedures whose MSPE improves as the number of covariates increase and this holds regardless of the type and percent of missingness.  ...

### Locality and low-dimensions in the prediction of natural experience from fMRI [article]

Francois G. Meyer, Greg J. Stephens
2008 arXiv   pre-print
We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction.  ...  We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features.  ...  FGM was partially supported by the Center for the Study of Brain, Mind and Behavior, Princeton University.  ...

### Tropical-cyclone intensification and predictability in three dimensions

Nguyen Van Sang, Roger K. Smith, Michael T. Montgomery
2008 Quarterly Journal of the Royal Meteorological Society
We present numerical-model experiments to investigate the dynamics of tropical-cyclone amplification and its predictability in three dimensions.  ...  The results provide new insight into the fluid dynamics of the intensification process in three dimensions, and at the same time suggest limitations of deterministic prediction for the mesoscale structure  ...  N00014-03-1-0185 from the US Office of Naval Research and by National Science Foundation Grants ATM-0715426, ATM-0649943, ATM-0649944, and ATM-0649946.  ...

### Modeling and predicting pointing errors in two dimensions

Jacob O. Wobbrock, Alex Jansen, Kristen Shinohara
2011 Proceedings of the 2011 annual conference on Human factors in computing systems - CHI '11
However, their model was based on one-dimensional (1-D) horizontal movement, while applications of such a model require two dimensions (2-D).  ...  For both univariate and bivariate models, the magnitudes of observed and predicted error rates are comparable.  ...  ACKNOWLEDGEMENTS The authors thank Edward Cutrell and I. Scott MacKenzie. This work was supported in part by the National Science Foundation under grants IIS-0811063 and IIS-0952786.  ...

### Prediction, Learning, Uniform Convergence, and Scale-Sensitive Dimensions

Peter L. Bartlett, Philip M. Long
1998 Journal of computer and system sciences (Print)
this algorithm in terms of a scale-sensitive generalization of the Vapnik dimension proposed by Alon, Ben-David, Cesa-Bianchi, and Haussler.  ...  We apply this result, together with techniques due to Haussler and to Benedek and Itai, to obtain new upper bounds on packing numbers in terms of this scale-sensitive notion of dimension.  ...  PREDICTION OF [0, 1]-VALUED FUNCTIONS AND fatV This section describes our general-purpose prediction strategy and shows that it is nearly optimal.  ...

### Gravitational uncertainties from dimension-six operators on supersymmetric GUT predictions

Alakabha Datta, Sandip Pakvasa, Uptal Sarkar
1995 Physical Review D, Particles and fields
We consider the gravity induced dimension six terms in addition to the dimension five terms in the SUSY GUT Lagrangian and find that the prediction for α_s may be washed out completely in supersymmetric  ...  Acknowledgement We would like to thank Prof.Xerxes Tata for useful discussions and Dr.Atanu Basu for computer assistance. This work was supported in part by US D.O.E under contract DE-AMO3-76SF-00325  ...  In this brief report we point out that for high GUT scale higher dimensional operators can be as significant as dimension five operators.  ...

### Unifying Lower Bounds on Prediction Dimension of Consistent Convex Surrogates [article]

Jessie Finocchiaro and Rafael Frongillo and Bo Waggoner
2021 arXiv   pre-print
We unify these settings using tools from property elicitation, and give a general lower bound on prediction dimension.  ...  Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research  ...  This state of affairs is especially dire when one seeks low prediction dimension, the dimension of the surrogate prediction domain.  ...
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