# how classification scores are interpreted?

I would like to know how to interpret classification scores (i am not sure about the word score or probability, please correct me). For example, for a binary classification positive values are labeled as 1, and -1 for negative ones. Now, is it fair to say that for a score 10 the instance is more likely to be successfully predicted than a score 5, despite the result that can be wrong.

Thanks.

If the scores have values that are higher than 1, I wouldn't call them probabilities. Probabilities should always be between 0 and 1.

And indeed, the higher the score, the more likely an example is to be positive, this is the most natural interpretation of a score.

I will try to answer your confusion but not the individual "how to" i.e. How a Decision Tree calculates probability etc. You may search the internet e.g. "How Decision Tree works etc."

Score is mostly used to describe the over-all prediction result of the model. There are many different techniques i.e. metrics for this e.g. Accuracy, RMS, ROCAUC depending upon the prediction type and some other specific conditions.

Probability tells us how confident the model is about its prediction.
Different models have different techniques to calculate the probability but in a very simple language, its proportional to the distance of the data points from the decision boundary the model has learnt from the training data.

As in the image, upper red-circled will have more probability of being "Yellow"

$$\hspace{4cm}$$

is it fair to say that for a score 10 the instance is more likely to be successfully predicted than a score 5

Yes, you can see that, the lower red circled point has more chance of being miss classified due to model bias.

• Thanks for the answer, by reading your response, i doubt if my score term definition is the correct one. My question is not about using metrics to evaluate the prediction results. Let's say, for instance, an SVM classifier ( or other models) with a score function that ouputs values not in the range of [0, 1], where positive ones are labeld as 1 and negative as -1. These values are not used to assess the model performance, they just tell us on which class belongs the prediction for a specefic instance. For sure, we can't call them probabilities but does the term score is correct in my case. – phillipe cauchett Jul 6 '20 at 11:38
• There are 3 steps(in general) - 1. First, the actual technical characteristics e.g. distance from support vector in case of SVM. 2. Then, using that get a probability(ignoring impl. detail, in some cases sigmoid, softmax are used). 3. Then a Threshold is used which is a hyper-parameter(you try multiple and check the best) e.g 0.4 > =1 <0.4 =0. Default is 0.5 ...So to summarize these 0,1 are derived from probability, we should rely more on probability. Just to avoid confusion - Some algo get the 0,1 naturally e.g. SVM and derivation is done for the probability – 10xAI Jul 6 '20 at 11:48
• "...but does the term score is correct in my case....", These should be called as Class e.g. 0-Fail, 1-Pass, Dog/Cat, Cancer/healthy etc. – 10xAI Jul 6 '20 at 11:52