Parity Learning

	Parity Learning Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ''ƒ'', given some samples (''x'', ''ƒ''(''x'')) and the assurance that ''ƒ'' computes the parity of bits at some fixed locations. The samples are generated using some distribution over the input. The problem is easy to solve using Gaussian elimination provided that a sufficient number of samples (from a distribution which is not too skewed) are provided to the algorithm. Noisy version ("Learning Parity with Noise") In Learning Parity with Noise (LPN), the samples may contain some error. Instead of samples (''x'', ''ƒ''(''x'')), the algorithm is provided with (''x'', ''y''), where for random boolean b \in \ y = \begin f(x), & \textb \\ 1-f(x), & \text \end The noisy version of the parity learning problem is conjectured to be hard and is widely used in cryptography. See also * Learning with errors In cryptography, learning with errors (LWE) is a ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Machine Learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Parity Function In Boolean algebra, a parity function is a Boolean function whose value is one if and only if the input vector has an odd number of ones. The parity function of two inputs is also known as the XOR function. The parity function is notable for its role in theoretical investigation of circuit complexity of Boolean functions. The output of the parity function is the parity bit. Definition The n-variable parity function is the Boolean function f:\^n\to\ with the property that f(x)=1 if and only if the number of ones in the vector x\in\^n is odd. In other words, f is defined as follows: :f(x)=x_1\oplus x_2 \oplus \dots \oplus x_n where \oplus denotes exclusive or. Properties Parity only depends on the number of ones and is therefore a symmetric Boolean function. The ''n''-variable parity function and its negation are the only Boolean functions for which all disjunctive normal forms have the maximal number of 2 ''n'' − 1 monomials of length ''n'' and al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Gaussian Elimination In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as possible. There are three types of elementary row operations: * Swapping two rows, * Multiplying a row by a nonzero number, * Adding a multiple of one row to another row. Using these operations, a matrix can always be transformed into an upper triangular matrix (possibly bordered by rows or columns of zeros), and in fact one that is in row echelon form. Once all of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Learning With Errors In cryptography, learning with errors (LWE) is a mathematical problem that is widely used to create secure encryption algorithms. It is based on the idea of representing secret information as a set of equations with errors. In other words, LWE is a way to hide the value of a secret by introducing noise to it. In more technical terms, it refers to the computational problem of inferring a linear n-ary function f over a finite Ring (mathematics), ring from given samples y_i = f(\mathbf_i) some of which may be erroneous. The LWE problem is conjectured to be hard to solve, and thus to be useful in cryptography. More precisely, the LWE problem is defined as follows. Let \mathbb_q denote the ring of integers Modular arithmetic, modulo q and let \mathbb_q^n denote the set of n-Vector (mathematics and physics), vectors over \mathbb_q . There exists a certain unknown linear function f:\mathbb_q^n \rightarrow \mathbb_q, and the input to the LWE problem is a sample of pairs (\mathbf,y), wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]