Adaptive imputation of missing values for incomplete pattern classification

In classification of incomplete pattern, the missing values can either play a crucial role in the class determination, or have only little influence (or eventually none) on the classification results according to the context. We propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory. At first, we try to classify the object (incomplete pattern) based only on the available attribute values. As underlying principle, we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information. In this case, the object is committed to this particular class. However, if the object cannot be classified without ambiguity, it means that the missing values play a main role for achieving an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is respectively classified according to each training class, and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (which are particular disjunctions of several single classes). The credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets

Electrostatic Field Classifier for Deficient Data

This paper investigates the suitability of recently developed models based on the physical field phenomena for classification problems with incomplete datasets. An original approach to exploiting incomplete training data with missing features and labels, involving extensive use of electrostatic charge analogy, has been proposed. Classification of incomplete patterns has been investigated using a local dimensionality reduction technique, which aims at exploiting all available information rather than trying to estimate the missing values. The performance of all proposed methods has been tested on a number of benchmark datasets for a wide range of missing data scenarios and compared to the performance of some standard techniques. Several modifications of the original electrostatic field classifier aiming at improving speed and robustness in higher dimensional spaces are also discussed

Theory-driven learning : using intra-example relationships to constrain learning

We describe an incremental learning algorithm, called theory-driven learning, that creates rules to predict the effect of actions. Theory-driven learning exploits knowledge of regularities among rules to constrain the learning problem. We demonstrate that this knowledge enables the learning system to rapidly converge on accurate predictive rules and to tolerate more complex training data. An algorithm for incrementally learning these regularities is described and we provide evidence that the resulting regularities are sufficiently general to facilitate learning in new domains

Utility indifference pricing with market incompleteness

Utility indifference pricing and hedging theory is presented, showing how it leads to linear or to non-linear pricing rules for contingent claims. Convex duality is first used to derive probabilistic representations for exponential utility-based prices, in a general setting with locally bounded semi-martingale price processes. The indifference price for a finite number of claims gives a non-linear pricing rule, which reduces to a linear pricing rule as the number of claims tends to zero, resulting in the so-called marginal utility-based price of the claim. Applications to basis risk models with lognormal price processes, under full and partial information scenarios are then worked out in detail. In the full information case, a claim on a non-traded asset is priced and hedged using a correlated traded asset. The resulting hedge requires knowledge of the drift parameters of the asset price processes, which are very difficult to estimate with any precision. This leads naturally to a further application, a partial information problem, with the drift parameters assumed to be random variables whose values are revealed to the hedger in a Bayesian fashion via a filtering algorithm. The indifference price is given by the solution to a non-linear PDE, reducing to a linear PDE for the marginal price when the number of claims becomes infinitesimally small

Informational Herding and Optimal Experimentation

We show that far from capturing a formally new phenomenon, informational herding is really a special case of single-person experimentation -- and 'bad herds' the typical failure of complete learning. We then analyze the analogous team equilibrium, where individuals maximize the present discounted welfare of posterity. To do so, we generalize Gittins indices to our non-bandit learning problem, and thereby characterize when contrarian behaviour arises: (i) While herds are still constrained efficient, they arise for a strictly smaller belief set. (ii) A log-concave log-likelihood ratio density robustly ensures that individuals should lean more against their myopic preference for an action the more popular it becomes.Bayesian learning, value function, herding, experimentation, log concavity, Gittins index, team equilibrium