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The problem of finding an optimal sparse coding with a given dictionary is known as sparse approximation (or sometimes just sparse coding problem). A number of algorithms have been developed to solve it (such as matching pursuit and LASSO ) and are incorporated in the algorithms described below.
Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. [1] Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and spare Bayesian inference [2]) on a library of nonlinear candidate functions of the snapshots against the ...
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.
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
In general, the risk () cannot be computed because the distribution (,) is unknown to the learning algorithm. However, given a sample of iid training data points, we can compute an estimate, called the empirical risk, by computing the average of the loss function over the training set; more formally, computing the expectation with respect to the empirical measure:
Empirically, for machine learning heuristics, choices of a function that do not satisfy Mercer's condition may still perform reasonably if at least approximates the intuitive idea of similarity. [6] Regardless of whether k {\displaystyle k} is a Mercer kernel, k {\displaystyle k} may still be referred to as a "kernel".
During the deep learning era, attention mechanism was developed to solve similar problems in encoding-decoding. [1] In machine translation, the seq2seq model, as it was proposed in 2014, [24] would encode an input text into a fixed-length vector, which would then be decoded into an output text. If the input text is long, the fixed-length vector ...
One example is the genetic algorithm for optimizing coefficients of a PID controller [2] or discrete-time optimal control. [3] Control design as regression problem of the first kind: MLC approximates a general nonlinear mapping from sensor signals to actuation commands, if the sensor signals and the optimal actuation command are known for every ...