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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Missing values : processing with the Kohonen algorithm
2007-01-05 · via math.ST updates on arXiv.org

The processing of data which contain missing values is a complicated and always awkward problem, when the data come from real-world contexts. In applications, we are very often in front of observations for which all the values are not available, and this can occur for many reasons: typing errors, fields left unanswered in surveys, etc. Most of the statistical software (as SAS for example) simply suppresses incomplete observations. It has no practical consequence when the data are very numerous. But if the number of remaining data is too small, it can remove all significance to the results. To avoid suppressing data in that way, it is possible to replace a missing value with the mean value of the corresponding variable, but this approximation can be very bad when the variable has a large variance. So it is very worthwhile seeing that the Kohonen algorithm (as well as the Forgy algorithm) perfectly deals with data with missing values, without having to estimate them beforehand. We are particularly interested in the Kohonen algorithm for its visualization properties.