Bayesian deep learning all too often underfits so that the Bayesian prediction is less accurate than a simple point estimate. Uncertainty quantification then comes at the cost of accuracy. For linearized models, the null space of the generalized Gauss-Newton matrix corresponds to parameters that preserve the training predictions of the point estimate. We propose to build Bayesian approximations in this null space, thereby guaranteeing that the Bayesian predictive does not underfit. We suggest a matrix-free algorithm for projecting onto this null space, which scales linearly with the number of parameters and quadratically with the number of output dimensions. We further propose an approximation that only scales linearly with parameters to make the method applicable to generative models. An extensive empirical evaluation shows that the approach scales to large models, including vision transformers with 28 million parameters.

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are treated as random variables with prior distributions, allowing for a probabilistic interpretation and quantification of predictive uncertainty. However, Bayesian methods lack theoretical generalization guarantees for unseen data. PAC-Bayesian analysis addresses this limitation by offering a frequentist framework to derive generalization bounds for randomized predictors, thereby certifying the reliability of Bayesian methods in machine learning. Temperature $T$, or inverse-temperature $\lambda = \frac{1}{T}$, originally from statistical mechanics in physics, naturally arises in various areas of statistical inference, including Bayesian inference and PAC-Bayesian analysis. In Bayesian inference, when $T < 1$ (``cold'' posteriors), the likelihood is up-weighted, resulting in a sharper posterior distribution. Conversely, when $T > 1$ (``warm'' posteriors), the likelihood is down-weighted, leading to a more diffuse posterior distribution. By balancing the influence of observed data and prior regularization, temperature adjustments can address issues of underfitting or overfitting in Bayesian models, bringing improved predictive performance.

Training your network the right way can make the difference between having a high-performance model, and having a failure of a model. There are several issues that may arise before and after training your network, that impairs its overall performance. However, the most well-known and also most prevalent issues are by far overfitting and underfitting.

This looks perfect and it clearly explains different type of cars. Let's try to decode what can overfitting and underfitting mean in Machine Learning. This definitions are subjective and it is being discussed only for novice learners to ML. On the First Day, when father is teaching her daughter, he hasn't picked an image with enough of car examples, which made daughter failed to generalize car object. On the Second Day, when father father is teaching her daughter, he has picked an images with cars and her daughter exactly learn the shape/type of car in the image, which forced her daughter to believe that car can only be of two shapes/types, which made her daughter failed to generalize car object.

In the previous courses, we have introduced linear and logistic regression, to model a Y variable which is discrete or continuous from one or more Xi variables, in all the examples used to illustrate this technique the modeling was relatively simple, the variable Y was generally modeled by a line parameterized by the variables Xi, but this modeling cannot be applied every time, an aquatic model must be chosen w.r.t to our data, in order to have the best fit. In this course we will study the effect of the choice of this modeling, we will see two cases, the first when the modeling is too weak to model our data, and the second is when the modeling is over-parameterized and that it will over-fit our data. Let's take a simple example and see what different modeling choices will produce in the fit of the data, we will use the following python code to generate and visualize the data, The figure above shows different fits for different choices of modeling assumptions, the first figure shows the simplest choice, modeling by a straight line of our data, in this case, we can notice that the modeling is very weak and we do not end with a good fit to our data, in this case, we are talking about underfitting, that is, the starting hypothesis is too weak for our data set. In this case, we notice that the modeling is over-parameterized, which gives an over-adjustment of our data without having a correct trajectory, we can notice that at the edge, we have a significant oscillation, which can mislead us if we want to predict the value of a new point which is at the edge, in this case, we speak of overfitting, that is to say, that our starting hypothesis is over-parameterized for our data. To sum up, when modeling data we can face two problems, first we can have a hypothesis that fails to model our data, and second, we can have a hypothesis that is over-parameterized and which will over-fit our data without the power to generalize to new examples, a trade-off must be made between the desired level of fit and the ability to generalize to new cases in order to have the best fit to the data.

Using recent machine learning results that present an information-theoretic perspective on underfitting and overfitting, we prove that deciding whether an encodable learning algorithm will always underfit a dataset, even if given unlimited training time, is undecidable. We discuss the importance of this result and potential topics for further research, including information-theoretic and probabilistic strategies for bounding learning algorithm fit.

In this article, we are going to indulge in two of the most discussed about and important concepts in machine learning which is related to the performance of a model. How do we know a model is performing better? Which model should we choose? For eg: I applied linear regression and decision tree algorithm on the train dataset of a classification problem. From above table, we can see that delta value from decision tree (5%) delta value from linear regression (20%), hence Decision would be perform best in this scenario. Note: Lower the delta value, higher the performance of the model.

So, the Solution is we need to split our data into training and testing sets. Training data (in-sample data) will be used to train our model and test data (out-of-sample) will be used for testing our model performance, this data will evaluate how our model performs on new sets or in real world. When we split a data, usually 70 percent of the data for training and 30 percent for testing. We will use sklearn for splitting our data, consider below code. And to help and validate our model python has a function which can be imported from sklearn library.

Splitting your data and having a Hold-Out process is undoubtedly the simplest model evaluation technique. We take our dataset and split it into two parts: A training set and a test set. After we generate a prediction from the training set, we test a model based on test set data that it has never been exposed to before to see if we get similar results. The typical procedure for this test is to set aside 10% to 30% of randomly chosen data or most recent data and leave it untouched until a model is built and ready to be deployed. Be careful though because if you keep tweaking your model based on the same hold out data then you may be lulled into using the test data to train your model and overfitting the model there without realizing it.