**PCNet**

A deep neural network (DNN) based power control method is proposed, which aims at solving the non-convex optimization problem of maximizing the sum rate of a multi-user interference channel. Towards this end, we first present PCNet, which is a multi-layer fully connected neural network that is specifically designed for the power control problem. PCNet takes the channel coefficients as input and outputs the transmit power of all users. A key challenge in training a DNN for the power control problem is the lack of ground truth, i.e., the optimal power allocation is unknown. To address this issue, PCNet leverages the unsupervised learning strategy and directly maximizes the sum rate in the training phase. Observing that a single PCNet does not globally outperform the existing solutions, we further propose ePCNet, a network ensemble with multiple PCNets trained independently. Simulation results show that for the standard symmetric multi-user Gaussian interference channel, ePCNet can outperform all state-of-the-art power control methods by 1.2%-4.6% under a variety of system configurations. Furthermore, the performance improvement of ePCNet comes with a reduced computational complexity. … **Lie Group Machine Learning (LML)**

In this paper a new method for dimensionality reduction in machine learning is pr oposed and called as Lie group Machine Learning (LML). The theory framework of LML is given , including the conception of one-parameter subgroup, Lie algebra and LML; the geometric properties of LML; the generalization hypothesis axiom, the partition independence hypothesis axiom, the duality hypothesis axiom, the learning compatibility hypothesis axiom of LML and the classifiers’ design of LML. The theory framework of Lie group machine learning (LML).

Survey on Lie Group Machine Learning … **Inductive Reasoning**

Inductive reasoning (as opposed to deductive reasoning or abductive reasoning) is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given. Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, though some sources disagree with this usage. The philosophical definition of inductive reasoning is more nuanced than simple progression from particular/individual instances to broader generalizations. Rather, the premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; that is, they suggest truth but do not ensure it. In this manner, there is the possibility of moving from general statements to individual instances (for example, statistical syllogisms, discussed below). …

# If you did not already know

**12**
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Nov 2018

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