All Questions
Tagged with expected-value machine-learning
47
questions
1
vote
2
answers
107
views
The training error of best hypothesis
Let $\mathcal{X}$ and $\mathcal{Y}$ denote the domain set and label set respectively. Also let $\mathcal{D}$ be a distribution over $\mathcal{X}$ and $f:\mathcal{X} \to \mathcal{Y}$ be the true ...
- 67
1
vote
0
answers
20
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Is There a Standard Metric for Evaluating Treatment Impact Considering Action Cost in Uplift Models?
I'm currently exploring Uplift modeling, specifically the use of the Conditional Average Treatment Effect (CATE) metric:
$$ \tau(t', t, x) := \mathbb{E}[Y | X=x, T=t'] - \mathbb{E}[Y | X=x, T=t] $$
...
- 57
0
votes
0
answers
19
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Find function $f$ such that the performance of models $h_1$ and $h_2$ is similar
Suppose that $h_1$ and $h_2$ are the first and third order polynomials respectively, which are obtained by solving the OLS equation (using the training dataset). Also consider the following ...
- 67
1
vote
1
answer
40
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Calibration Expectation Decompostion
I am reading a "Calibrated Structured Prediction by Kuleshov and Liang" link.
Calibration and sharpness. Given a forecaster $F : X → [0, 1]$, define $T(x) = \mathbb{E}[y| F(x)]$ to be the ...
- 11
2
votes
1
answer
246
views
Monte-Carlo integration with importance-sampling
I came across a paper, where (section 3.2) importance sampling is used to estimate an integral. I think I understand what importance sampling is but I don't understand how they got the solution.
The ...
- 23
1
vote
0
answers
21
views
Optimizing Algorithmic Trading Parameters: A Quest for Maximizing Expected Value
I am engaged in algorithmic trading, employing specialized models that utilize various parameters to signal trading opportunities. Once I get a signal, I could execute a trade and everything is ...
- 11
1
vote
0
answers
24
views
An Alternative In-sample-goodness-of-fit Measure in Machine Learning Methods for Estimating Heterogeneous Causal Effects Paper
In 3.5.2 of Machine Learning Methods for Estimating Heterogeneous Causal
Effects by Susan Athey and Guido Imbens it is stated:
"If the models include an intercept, as they usually do, most ...
- 43
3
votes
1
answer
262
views
Sum of probabilities of all samples gives the total volume?
I am working on a churn problem (binary classification - whether a customer will churn or not). Now using logistic regression, I get the probability whether the customer will churn or not.
Can I add ...
- 85
0
votes
1
answer
793
views
What do "Expectation" mean in cost function?
I want to know whether my understanding for expectation of loss function is correct or not.
(x,y) means sample data-label distribution from true distribution. And function f which is respect to ...
6
votes
1
answer
242
views
True Error in Machine Learning
I have read this question and I am confused by a part of the first answer, even though it is asked in the comments.
I don't understand why $$L_{(\mathcal{D}, f)}(h^{*}) = 0 \implies L_{S}(h^{*}) = 0$$
...
- 309
18
votes
3
answers
2k
views
Why do we care more about test error than expected test error in Machine Learning?
In Section 7.2 of Hastie, Tibshirani, and Friedman (2013) The Elements of Statistic Learning, we have the target variable $Y$, and a prediction model $\hat{f}(X)$ that has been estimated from a ...
- 817
2
votes
1
answer
120
views
Statistical learning and expected value
I'm studying some statistical learning theory. If i have $X$, $Y$ as random variables representing the data-labels samples drawn from a certain distribution and a loss function, it is right to say ...
- 23
2
votes
1
answer
698
views
how is the expectation of the empirical error based on an i.i.d. sample S is equal to the generalization error?
I am on the 28 page of the book called "foundations of machine learning" by M.Mohri which states that for a fixed hypothesis h,the expected value of the empirical error is equal to ...
- 45
3
votes
1
answer
61
views
Expected square error formula
I am going through this blog post to understand the Variance - Bias Tradeoff. In this, the author mentions:
Err(x) = E[(Y - f'(x))^2]
I understand this. But then, ...
2
votes
1
answer
144
views
Derivation of expected loss ESL (integrating over conditional expectation confusion)
I am trying to understand the derivation of expected loss (equation 2.11 in Elements of Statistical learning) and there is a specific step I do not understand.
We start with
$EPE(f) = E(Y - f(x))^{2}$
...
- 341