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Full-Text Articles in Mathematics
Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich
Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical problems, the most effective classification techniques are based on deep learning. In this approach, once the neural network generates values corresponding to different classes, these values are transformed into probabilities by using the softmax formula. Researchers tried other transformation, but they did not work as well as softmax. A natural question is: why is softmax so effective? In this paper, we provide a possible explanation for this effectiveness: namely, we prove that softmax is the only consistent approach to probability-based classification. In precise terms, it is the only approach for which two reasonable probability-based ideas -- Least …
A Gibbs Sampling Approach To Maximum A Posteriori Time Delay And Amplitude Estimations, Michele Picarelli
A Gibbs Sampling Approach To Maximum A Posteriori Time Delay And Amplitude Estimations, Michele Picarelli
Dissertations
Research concerned with underwater propagation in a shallow ocean environment is a growing area of study. In particular, the development of fast and accurate computational methods to estimate environmental parameters and source location is desired. In this work, only select features of the acoustic field are investigated, namely, the time delays and amplitudes of individual paths, the signal-to-noise ratio, and the number of multi-path arrivals. The amplitudes and delays contain pertinent information about the geometry associated with the environment of interest. Estimating the time delays and amplitudes of select paths in a manner that is both accurate and time efficient, …