Above are papers related to the following paper: [Paper_ID] Paper #1107558. 	[Title] Bits-back coding software guide [Abstract] Abstract | In this document, I first review the theory behind bits-back coding (aka. free energy coding) (Frey and Hinton 1996) and then describe the interface to C-language software that can be used for bits-back coding. This method is a new approach to the problem of optimal compression when a source code produces multiple codewords for a given symbol. It may seem that the most sensible codeword to use in this case is the shortest one. However, in the proposed bits-back approach, random codeword selection yields an effective codeword length that can be less than the shortest codeword length. If the random choices are Boltzmann distributed, the effective length is optimal for the given source code. The software which I describe in this guide is easy to use and the source code is only a few pages long. I illustrate the bits-back coding software on a simple quantized Gaussian mixture problem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #41216. 	[Title] A simple algorithm that discovers efficient perceptual codes [Abstract] We describe the "wake-sleep" algorithm that allows a multilayer, unsupervised, neural network to build a hierarchy of representations of sensory input. The network has bottom-up "recognition" connections that are used to convert sensory input into underlying representations. Unlike most artificial neural networks, it also has top-down "generative" connections that can be used to reconstruct the sensory input from the representations. In the "wake" phase of the learning algorithm, the network is driven by the bottom-up recognition connections and the top-down generative connections are trained to be better at reconstructing the sensory input from the representation chosen by the recognition process. In the "sleep" phase, the network is driven top-down by the generative connections to produce a fantasized representation and a fantasized sensory input. The recognition connections are then trained to be better at recovering the fantasized representation from the fantasized sensory input. In both phases, the synaptic learning rule is simple and local. The combined effect of the two phases is to create representations of the sensory input that are efficient in the following sense: On average, it takes more bits to describe each sensory input vector directly than to first describe the representation of the sensory input chosen by the recognition process and then describe the difference between the sensory input and its reconstruction from the chosen representation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #62417. 	[Title] Free energy coding  In [Abstract] In this paper, we introduce a new approach to the problem of optimal compression when a source code produces multiple codewords for a given symbol. It may seem that the most sensible codeword to use in this case is the shortest one. However, in the proposed free energy approach, random codeword selection yields an effective codeword length that can be less than the shortest codeword length. If the random choices are Boltzmann distributed, the effective length is optimal for the given source code. The expectation-maximization parameter estimation algorithms minimize this effective codeword length. We illustrate the performance of free energy coding on a simple problem where a compression factor of two is gained by using the new method. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4335. 	[Title] A VIEW OF THE EM ALGORITHM THAT JUSTIFIES INCREMENTAL, SPARSE, AND OTHER VARIANTS [Abstract] The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. Please summarise all the given information.

Paper #1107558 has the title `Bits-back coding software guide  
` and the abstract `Abstract | In this document, I first review the theory behind bits-back coding (aka. free energy coding) (Frey and Hinton 1996) and then describe the interface to C-language software that can be used for bits-back coding. This method is a new approach to the problem of optimal compression when a source code produces multiple codewords for a given symbol. It may seem that the most sensible codeword to use in this case is the shortest one. However, in the proposed bits-back approach, random codeword selection yields an effective codeword length that can be less than the shortest codeword length. If the random choices are Boltzmann distributed, the effective length is optimal for the given source code. The software which I describe in this guide is easy to use and the source code is only a few pages long. I illustrate the bits-back coding software on a simple quantized Gaussian mixture problem. 
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Question: Which category should Paper #1107558 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1107558 has the title `Bits-back coding software guide  
` and the abstract `Abstract | In this document, I first review the theory behind bits-back coding (aka. free energy coding) (Frey and Hinton 1996) and then describe the interface to C-language software that can be used for bits-back coding. This method is a new approach to the problem of optimal compression when a source code produces multiple codewords for a given symbol. It may seem that the most sensible codeword to use in this case is the shortest one. However, in the proposed bits-back approach, random codeword selection yields an effective codeword length that can be less than the shortest codeword length. If the random choices are Boltzmann distributed, the effective length is optimal for the given source code. The software which I describe in this guide is easy to use and the source code is only a few pages long. I illustrate the bits-back coding software on a simple quantized Gaussian mixture problem. 
`.
Question: Which category should Paper #1107558 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods