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Model order reduction aims to lower the computational complexity of such problems, for example, in simulations of large-scale dynamical systems and control systems. By a reduction of the model's associated state space dimension or degrees of freedom , an approximation to the original model is computed which is commonly referred to as a reduced ...
The function : is often referred to as a kernel or a kernel function. The word "kernel" is used in mathematics to denote a weighting function for a weighted sum or integral . Certain problems in machine learning have more structure than an arbitrary weighting function k {\displaystyle k} .
In addition to the supervised learning setting, sample complexity is relevant to semi-supervised learning problems including active learning, [7] where the algorithm can ask for labels to specifically chosen inputs in order to reduce the cost of obtaining many labels.
Kernelization is often achieved by applying a set of reduction rules that cut away parts of the instance that are easy to handle. In parameterized complexity theory, it is often possible to prove that a kernel with guaranteed bounds on the size of a kernel (as a function of some parameter associated to the problem) can be found in polynomial time.
It is impossible to count the number of steps of an algorithm on all possible inputs. As the complexity generally increases with the size of the input, the complexity is typically expressed as a function of the size n (in bits) of the input, and therefore, the complexity is a function of n. However, the complexity of an algorithm may vary ...
Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting.
Many-one reductions are valuable because most well-studied complexity classes are closed under some type of many-one reducibility, including P, NP, L, NL, co-NP, PSPACE, EXP, and many others. It is known for example that the first four listed are closed up to the very weak reduction notion of polylogarithmic time projections.
Mamba [a] is a deep learning architecture focused on sequence modeling. It was developed by researchers from Carnegie Mellon University and Princeton University to address some limitations of transformer models , especially in processing long sequences.