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The effective fractal dimensions at the polynomial-space level and above can all be equivalently defined as the C-entropy rate where C is the class of languages corresponding to the level of effectivization. For example, pspace-dimension is equivalent to the PSPACE-entropy rate. At lower levels of complexity the equivalence proofs break down. In the… (More)

Significant changes in the instance distribution or associated cost function of a learning problem require one to reoptimize a previously learned classifier to work under new conditions. We study the problem of reoptimizing a multi-class classifier based on its ROC hypersurface and a matrix describing the costs of each type of prediction error. For a binary… (More)

We make progress in understanding the complexity of the graph reachability problem in the context of unambiguous logarithmic space computation; a restricted form of nondeterminism. As our main result, we show a new upper bound on the <i>directed planar reachability problem</i> by showing that it can be decided in the class unambiguous logarithmic space… (More)

We explore the problem of budgeted machine learning, in which the learning algorithm has free access to the training examples' labels but has to pay for each attribute that is specified. This learning model is appropriate in many areas, including medical applications. We present new algorithms for choosing which attributes to purchase of which examples in… (More)

Designing algorithms that use logarithmic space for graph reachability problems is fundamental to complexity theory. It is well known that for general directed graphs this problem is equivalent to the NL vs L problem. This paper focuses on the reachability problem over planar graphs where the complexity is unknown. Showing that the planar reachability… (More)

- Kun Deng, Chris Bourke
- 2006

We study the problem of optimizing a multi-class classifier based on its ROC hypersur-face and a matrix describing the costs of each type of prediction error. For a binary classi-fier, it is straightforward to find an optimal operating point based on its ROC curve and the relative cost of true positive to false positive error. However, the corresponding… (More)

We explore the problem of budgeted machine learning, in which the learning algorithm has free access to the training examples’ class labels but has to pay for each attribute that is specified. This learning model is appropriate in many areas, including medical applications. We present new algorithms for choosing which attributes to purchase of which… (More)

- Chris Bourke
- 2007

We extend previous collapsing results involving the exponential hierarchy by using recent hardness-randomness trade-off results. Specifically, we show that if the second level of the exponential hierarchy has polynomial-sized circuits, then it collapses all the way down to MA.

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