13
votes
Accepted
Are softmax outputs of classifiers true probabilities?
The answer is both yes, and no. Or, to put it another way, the answer depends on what exactly you mean by "represent probabilities", and there is a valid sense in which the answer is yes, ...
- 266
11
votes
Are softmax outputs of classifiers true probabilities?
Excellent question.
The simple answer is no. Softmax actually produces uncalibrated probabilities. That is, they do not really represent the probability of a prediction being correct.
What usually ...
- 1,112
10
votes
Accepted
What is a Markov chain and how can it be used in creating artificial intelligence?
A Markov model includes the probability of transitioning to each state considering the current state. "Each state" may be just one point - whether it rained on specific day, for instance - or it might ...
- 2,569
8
votes
Is Nassim Taleb right about AI not being able to accurately predict certain types of distributions?
Yes and no!
There's no inherent reason that machine learning systems can't deal with extreme events. As a simple version, you can learn the parameters of a Weibull distribution, or another extreme ...
- 9,037
5
votes
Accepted
How can supervised learning be viewed as a conditional probability of the labels given the inputs?
This formulation/interpretation can indeed be confusing (or even misleading), as the output of a neural network is usually deterministic (i.e. given the same input $x$, the output is always the same, ...
- 37k
3
votes
Accepted
How to calculate probability from fuzzy membership grade?
No, you can't extract any probability from a fuzzy membership grade. The uncertainty expressed by fuzzy logic is about partial truth, not about probability. $ \mu_S(x) = 0.9 $ doesn't mean that "$...
- 436
3
votes
Accepted
How does $\mathbb{E}$ suddenly change to $\mathbb{E}_{\pi'}$ in this equation?
Also, in general, in the conditional expectation, which distribution do we compute the expectation with respect to? From what I have seen, in $\mathbb{E}[X|Y]$, we always calculate the expected value ...
- 4,420
3
votes
The problem with the Gambler's Problem in RL
The intuitive explanation is that there are many equally good "optimal" policies. This is mentioned at the end of the example problem description you posted. My gut says that the family of optimal ...
- 9,037
3
votes
What does the argmax of the expectation of the log likelihood mean?
This equation and more information of it can be found in Expectation Maximization Wikipedia site and the explanation there was as follows (formula there in two parts):
Some more explanation from same ...
- 927
2
votes
Are probabilistic models dead ends in AI?
I think Minsky deprecated the suggestion that probabilistic models could be surrogates for component models for intelligence that he suggested were grounded in principles and processes that interact (...
- 679
2
votes
Are probabilistic models dead ends in AI?
When considering effective approaches to AGI, one must extrapolate outwards to the types of modelling (and therefore inputs) that would be necessary to achieve any general utility. One consideration ...
- 51
2
votes
What is a Markov chain and how can it be used in creating artificial intelligence?
(this was intended as a comment, but turned out long and longer)
A couple of points to elaborate on Ben's answer:
It is possible to generate different models (out of existing data!) and then look ...
- 538
2
votes
What are the meanings of these (P(x;y), P(x;y,z),P(x,y;z))?
This means "Parameterized by".
First, we all agree on the idea of conditional probabilities:
$$P(X | Y) = P(X,Y) / P(Y)$$
That is, the probability that X happens given that we've seen Y happen, is ...
- 9,037
2
votes
How do I combine two electromagnetic readings to predict the position of a sensor?
Position Detection
In a traditional data acquisition and control scenario, with some assumptions, the relation between sensors signals $s_i$, emitters drive $\epsilon_j$, distances $x_{ij}$, and ...
- 7,375
2
votes
Viterbi versus filtering
Welcome to AI.SE @vdbuss, and great first question!
This point is touched on in Section 15.2.3 (page 576 in my copy), in the second paragraph, and there's a good exercise at the end of the chapter (...
- 9,037
2
votes
How to make machine learning model that reports ambiguity of the input?
Another specific way to do this if one uses a neural network for this. Use a dropout a layer in your network and instead of scaling the activations at test time, one can sample the activations (just ...
- 404
2
votes
Accepted
How do I calculate the probabilities of the BERT model prediction logits?
Your call to model.predict() is returning the logits for softmax. This is useful for training purposes.
To get probabilties, you need to apply softmax on the logits....
- 26.6k
2
votes
Accepted
How to classify data into organised groups by using a resulting classification vector and a set of probabilities?
To transform your logits [-5,1,2] into probabilities you can use the softmax function. This would get you ...
- 882
2
votes
Accepted
What are the prerequisites to start using the TensorFlow Probability library?
Although this question is slightly primarily opinion-based and too broad (and I will probably close it as such) and a good answer will necessarily depend on your background, I will list some of the ...
- 37k
2
votes
What exactly is a Parzen?
Parzen was a statistician, who worked in spectral analysis and stochastic processes. I don't know if he invented them, but those windows and probability density esimation methods are named after him.
...
- 5,252
2
votes
What makes ChatGPT a generative model?
They both refer to the same type of models. However, the second definition is a more 'intuitive' explanation of what generative AI does, while the first is a definition that refers more to what a ...
- 808
2
votes
What makes ChatGPT a generative model?
What are generative (and discriminative) models?
If the model learns a distribution of the form $p(x)$ or $p(x, y)$, where $x$ are the inputs and $y$ the outputs/labels, from which you can sample data,...
- 37k
1
vote
What does the product of probabilities raised to own powers used for entropy calculation quantify?
I don't know if $N(X)$ has a name or has any applicability in AI, but I can comment on how this function varies as the $H(X)$ based on your equation
$$N(X) = \dfrac{1}{2^{H(X)}}$$
which looks correct ...
- 37k
1
vote
Does generator in conditonal GAN obey probability laws?
I don't see where it's implied that G is a probability distribution. G is a function, whose output conditioned on one variable has a probability distribution, but it isn't one.
z is random noise which ...
- 659
1
vote
Accepted
Aren't scores in the Wasserstein GAN probabilities?
Figure 3 in the original WGAN paper is actually quite helpful to understand the difference between the score in WGAN and the probability in GAN (see screenshot below). The blue distribution are real ...
- 144
1
vote
Accepted
How can I convert the probability score between 0 to 1 to another format?
You could maybe do something like this, it's a bit hackish
\begin{equation}
y = C_1\cdot 1 + C_2 \cdot 0.5 + C_3 \cdot 0
\end{equation}
$y$ represents the output and its bounded $\in [0, 1]$. $C_i$ is ...
- 2,286
1
vote
Is there an AI model with "certainty" built in?
You make a valid point, vanilla neural networks cannot give you more than a point estimate of class confidence. If one wanted to actually gain an idea of variance, you need a framework that allows ...
- 2,339
1
vote
Accepted
Why is probability that at least one hypothesis out of $k$ being consistent with $m$ training examples $k(1- \epsilon)^m$?
Let $A$ and $B$ be two events. In general, the probability that either $A$ or $B$ occurs is defined as
$$
P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)
$$
If $A$ and $B$ are disjoint, i.e. ...
- 37k
1
vote
Why does the error ensemble use the ceiling of the number of classifiers?
Y ensemble size voting wrong
k = 50% or majority threshold
If you have 11 models. Then the majority of models is anything bigger than 50% of the number of ensemble models. In the example where ...
- 119
1
vote
How to make machine learning model that reports ambiguity of the input?
Predicting with confidence: the best machine learning idea you never heard of by Scott Locklin might provide you an idea.
The name of this basket of ideas is “conformal prediction.”
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