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In machine learning, the term bias can refer to at least 2 related concepts A (learnable) parameter of a model, such as a linear regression model, which allows you to learn a shifted function. For example, in the case of a linear regression model $y = f(x) = mx + b$, the bias $b$ allows you to shift the straight-line up an down: without the bias, you would ...


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Imagine we have the curve $f(x) = x^2$, and we want to find the minimum of this function. The derivate of $f$ with respect to $x$ is $2x$. Now, gradient descent works by updating our current estimate of the minimum, say $c_t$, by the following iterative process $$c_{t+1} = c_t - \alpha \times \nabla_xf(x=c_t),$$ where $\alpha$ is some constant to control how ...


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A neural network can be reduced to a linear regression model only if we use linear activation functions (i.e. $\sigma(x) = x$), and only if we do not use any neural network specific techniques such as convolution, residuals, etc., as shown below: $\text{neural network}(x) = \sigma_n(W_{n} \sigma_{n-1}(W_{n-1}\dots\sigma_1(W_1 x + b_1) + \dots + b_{n-1}) + ...


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Sorry if this is a bad use of answer to add comment but since my reputation is not high enough this is only way to leave a comment to OP's question. I think some of the answers misunderstood the OP's intention. Over fitting is used as a means to test the complexity of the model - if a model cannot overfit a small dataset then it's likely not able to ...


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In some cases, you can solve a linear regression problem with an analytical (or closed-form) solution/expression (although this may not always be the best approach). See this answer for more details. Note that this solution involves matrix multiplications and the computation of an inverse with floating-point numbers, so this is still a numerical algorithm/...


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Honourable mention: Memory-based approaches Although not analytic, memory-based models, such as k-nearest neighbours (k-NN) are very lightweight when learning, but have a higher cost to use the stored knowledge. Even though a k-NN model is slow to make inferences, the computation involved is not complex or iterative. It makes a single pass through all the ...


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The answer is largely the same whether we consider $\ell_1$ or $\ell_2$ regularisation, so I will just speak generally about regularisation. Mean square error for training data Given some training data $\{(x_i, y_i)\}_{i = 1}^n$, a linear regression line $Y = aX + b$ fit using the least squares method looks for coefficients that minimise the sum of squares, ...


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OK, so I found the answer - it is to use multiple linear regression. I think this can be marked a solved, but I don't have enough rep to do that.


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RLS is a second order optimizer, so, unlike LMS which takes into account an approximation of the derivative of the gradient, RLS also considers the second order derivative. You can study more about second order methods in sub-section "8.6 Approximate Second-Order Methods" of the following book available online: https://www.deeplearningbook.org/...


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