**logistic sigmoid function**to return a probability value.

Which function returns the numeric position of a named string?

**what is character function**.

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The cost function used in Logistic Regression is **Log Loss**.

**Log Loss** is the loss function for logistic regression. Logistic regression is widely used by many practitioners.

**log(p/1-p)** is the link function. Logarithmic transformation on the outcome variable allows us to model a non-linear association in a linear way. This is the equation used in Logistic Regression. Here (p/1-p) is the odd ratio.

Unlike linear regression which outputs continuous number values, logistic regression **transforms its output** using the logistic sigmoid function to return a probability value which can then be mapped to two or more discrete classes.

The square, hinge, and logistic functions share the **property of being convex** . … Formal definition : f is convex if the chord joining any two points is always above the graph. ► If f is differentiable, this is equivalent to the fact that the derivative. function is increasing.

Logistic regression cost function has local minima (or has no global minimum). Therefore, logistic regression cost function is a **non-convex function**.

Regularization **can be used to avoid overfitting**. In other words: regularization can be used to train models that generalize better on unseen data, by preventing the algorithm from overfitting the training dataset. …

Most importantly we see that the dependent variable in logistic regression follows Bernoulli distribution having an unknown probability P. Therefore, the logit i.e. **log of odds**, links the independent variables (Xs) to the Bernoulli distribution.

Logistic Regression is one of the basic and popular algorithms to solve a classification problem. It is named ‘Logistic Regression’ **because its underlying technique is quite the same as Linear Regression**. The term “Logistic” is taken from the Logit function that is used in this method of classification.

It can be used for Classification as well as for Regression problems, but mainly used for **Classification problems**. Logistic regression is used to predict the categorical dependent variable with the help of independent variables. The output of Logistic Regression problem can be only between the 0 and 1.

- Step 1: Import Packages. All you need to import is NumPy and statsmodels.api : …
- Step 2: Get Data. You can get the inputs and output the same way as you did with scikit-learn. …
- Step 3: Create a Model and Train It. …
- Step 4: Evaluate the Model.

Logistic Regression is another statistical analysis method borrowed by Machine Learning. It is used **when our dependent variable is dichotomous or binary**. It just means a variable that has only 2 outputs, for example, A person will survive this accident or not, The student will pass this exam or not.

The main reason why we use sigmoid function is **because it exists between (0 to 1)**. Therefore, it is especially used for models where we have to predict the probability as an output. Since probability of anything exists only between the range of 0 and 1, sigmoid is the right choice.

True, Logistic regression is **a supervised learning algorithm** because it uses true labels for training. Supervised learning algorithm should have input variables (x) and an target variable (Y) when you train the model .

The short answer is: Logistic regression is **considered a generalized linear model** because the outcome always depends on the sum of the inputs and parameters. Or in other words, the output cannot depend on the product (or quotient, etc.) … Logistic regression is an algorithm that learns a model for binary classification.

Now, since a linear combination of two or more **convex** functions is convex, we conclude that the objective function of logistic regression is convex. Following the same line of approach/argument it can be easily proven that the objective function of logistic regression is convex even if regularization is used.

An important note about the logistic function is that it has an **inflection point**. From the previous graph you can observe that at the point (0, 1) the graph transitions from curving up (concave up) to curving down (concave down).

Hence we have to check that if H(ŷ) is positive for all values of “x” or not, to be a convex function. We know that y can take two values 0 or 1. … Hence, based on the convexity definition we have mathematically shown the MSE loss function for **logistic regression is non-convex and not recommended**.

Log odds play an important role in logistic regression as **it converts the LR model from probability based to a likelihood based model**. … Thus, using log odds is slightly more advantageous over probability. Before getting into the details of logistic regression, let us briefly understand what odds are.

One of the main reasons why **MSE doesn’t work with logistic regression** is when the MSE loss function is plotted with respect to weights of the logistic regression model, the curve obtained is not a convex curve which makes it very difficult to find the global minimum.

In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. … A sigmoid function is **convex for values less than a particular point**, and it is concave for values greater than that point: in many of the examples here, that point is 0.

Logistic regression **turns the linear regression framework into** a classifier and various types of ‘regularization’, of which the Ridge and Lasso methods are most common, help avoid overfit in feature rich instances.

A regression model that uses L1 regularization technique is called **Lasso Regression** and model which uses L2 is called Ridge Regression. The key difference between these two is the penalty term. Ridge regression adds “squared magnitude” of coefficient as penalty term to the loss function.

My main aim in this post is to provide a beginner level introduction to logistic regression using R and also introduce LASSO (Least Absolute Shrinkage and Selection Operator), a powerful feature selection technique that is very useful for **regression problems**. Lasso is essentially a regularization method.

FIGURE 5.6: The logistic function. It outputs **numbers between 0 and 1**. … For classification, we prefer probabilities between 0 and 1, so we wrap the right side of the equation into the logistic function. This forces the output to assume only values between 0 and 1.

The output from the logistic regression analysis gives **a p-value of** , which is based on the Wald z-score. Rather than the Wald method, the recommended method to calculate the p-value for logistic regression is the likelihood-ratio test (LRT), which for this data gives .

The purpose of the logit link is **to take a linear combination of the covariate values (which may take any value between ±∞) and convert those values to the scale of a probability, i.e., between 0 and 1.**

Some of the popular types of regression algorithms are **linear regression**, regression trees, lasso regression and multivariate regression.

Linear Regression is used to **handle regression problems** whereas Logistic regression is used to handle the classification problems. Linear regression provides a continuous output but Logistic regression provides discreet output.

Which of the following function is used by logistic regression to convert the probability in the range between [0,1]? a) Sigmoid b) Mode c) Square d) Probit Answer: **A Sigmoid function** is used to convert output probability between [0, 1] in logistic regression.

Unlike linear regression models, which are used to predict a continuous outcome variable, logistic regression models are **mostly used to predict a dichotomous categorical outcome**, LRAs are frequently used in business analysis applications. An application may use logistic analysis to determine consumer behavior.

Logistic regression is **a supervised learning classification algorithm used to predict the probability of a target variable**. … It is one of the simplest ML algorithms that can be used for various classification problems such as spam detection, Diabetes prediction, cancer detection etc.

Logistic regression is usually used with binary response variables ( 0 or 1 ), the **predictors can be continuous or discrete**.

Leaky ReLU. Leaky ReLUs are **one attempt to fix the “dying ReLU” problem**. Instead of the function being zero when x < 0, a leaky ReLU will instead have a small positive slope (of 0.01, or so).

The activation function is a node that is put at the end of or in between Neural Networks. They help to decide if the neuron would fire or not. “The activation function is **the non linear transformation that we do over the input signal**. This transformed output is then sent to the next layer of neurons as input.” —

Simply put, an activation function is a **function that is added into an artificial neural network in order to help the network learn complex patterns in the data**. When comparing with a neuron-based model that is in our brains, the activation function is at the end deciding what is to be fired to the next neuron.