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You are looking for scoring-rules, which do precisely what you want: they assess the quality probabilistic predictions. Specifically, you want proper scoring rules, which are scoring rules that are optimized on the "correct" probabilistic predictions. Here is Wikipedia. The simplest one you could use would be the logarithmic score, which is $\log P_A$ if ...


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What you described is not an imbalanced classification problem. Positive vs. negative is 2:1 is a well balanced dataset and most models (such as logistic regression) will be perfectly fine. Usually when talking about the imbalanced problem people are talking about 1000:1 or even worse. Think about the credit card fraud detection problem, where most ...


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Keep the all data! Making your groups "equally bad" serves no mathematical purpose! And in Biological context you wouldn't survive peer-review removing data without a strong justification! Never do that! After doing Levene and Shapiro, it's legitimate to use ANOVA on different sample sizes!


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Whatever you do, you should not falsify your data by producing (somehow?) a new, balanced dataset. You have the data you have, and must live with it! While anova methods are more powerful (and robust) with balanced data, they can work and be used with unbalanced data. And the unbalance in your dataset does not seem to be very bad. As for practical advice, ...


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When we're talking about the estimated parameters of a neural network, a "bias" is any constant that's added to an input. Consider logistic regression, i.e. a neural network without hidden layers and a single, sigmoidal output. This network has the prediction equation $$ \hat{y} = \sigma(w^\top x+b) $$ where $x$ is the input vector, $w$ is the vector ...


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The snippet you are showing takes is a layer that takes the output of a 16-dimensional hidden layer (let's call it $\mathbf{h}$) and does the following: $$o = \sigma\left( \mathbf{w}^\top\mathbf{h} + b \right)$$ where $\mathbf{w} \in \mathbb{R}^{16}$ is the weight vector (inside fo TF is a matrix with a single row) and $b \in \mathbb{R}$ is the bias. The ...


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