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It's the law of total probability, combined with the definition of conditional probability. \begin{align*} p(x_n) = \int_{x_{n-1}} p(x_n, x_{n-1}) = \int_{x_{n-1}} p(x_n \, | \, x_{n-1})p(x_{n-1}) \end{align*} First equality uses the law of total probability, second uses definition of conditional probability. The only difference in the paper, is that ...

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Definitely yes. I would say Transformers would work wherever LSTM works and even better. The reason is that they can attend to longer sequences as an input. In contrast to transformers, in LSTM for example after some sequence length(in your case the signal length) it would lose performance. No, I don't specifically know projects that are in this domain.But ...

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In simple terms, without this transformation the network doesn't know that 2022-01-01 data likely correlates with the January 1st on previous (and future!) years. And actually it is likely to also correlate with January 3rd, and maybe even December 29th. It is also possible to encode the day of year as float between 0.0 and 1.0 (first day of year and last ...

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Sorry for my weak English. Your are using neural network to forecast times series which often have irregular fluctuations. Stock values are volatile and have changing frequency. Applying periodic encodings to original data makes it easier to capture frequency information. Read this paper to understand why it is essential for the neural network to know about ...

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I don't think time series model necessarily makes sense if you have one conductivity value to predict for each time series. A regression like setup makes more sense here: you could model this by letting the vector of time points represent the input. So you'd end up with a $n \mbox{ x } t$ matrix as input to predict the conductivity value.

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