"Missing { inserted" in align* environment

Question

I have this bit of code:

\begin{align*} 
P(\omega_{k}|x) \approx \hat{y_k}(x) = \frac{exp(w^{T}_{k}x^')}{\sum^{q}_{j=1}exp(w^{T}_{j}x^')} 
\\
where \quad x^' = [1, x_1, x_2,...,x_p]^T\quad\\ 
with \quad 0 \leq \hat{y_k}(x) \leq 1 \quad and \quad \sum^{q}_{k=1} \hat{y_k}(x) = 1 
\end{align*}

That keeps sending me the following error message:

"! Missing { inserted. ^ l.295 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.)"

I have no idea of to fix this as I am a new user of LaTeX... Could someone please help me? Thanks

Answer 1

OK, @Johannes_B has already given you some advice. Meanwhile, I was trying to to tidy up your code: see if I have guessed your intentions correctly.

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.

\usepackage[ascii]{inputenc}     % Just to check that the source is still pure,
                                 % 7-bit-clean ASCII when you execute it, as it
                                 % was when I wrote it.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{mathtools}



\begin{document}

Text before.
\begin{gather*} 
P(\omega_{k}|x) \approx \widehat{y_k}(x)
    = \frac{\exp(w^{T}_{k}x')}{\sum^{q}_{j=1}\exp(w^{T}_{j}x')}  \\[\jot]
\text{where} \quad x' = [1, x_1, x_2,\dots,x_p]^T  \\ 
\text{with} \quad 0 \leq \widehat{y_k}(x) \leq 1 \quad
\text{and} \quad \sum^{q}_{k=1} \widehat{y_k}(x) = 1 
\end{gather*}
Text after.

\end{document}

Anyway, I’d use a different approach, separating the part after “where” in another equation.

Addendum: Another possibility, using the split environment. Note also the introduction of a higher level of abstraction, by means of the \innerprod command.

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.

\usepackage[ascii]{inputenc}     % Just to check that the source is still pure,
                                 % 7-bit-clean ASCII when you execute it, as it
                                 % was when I wrote it.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{mathtools}

\DeclarePairedDelimiterX{\innerprod}[2]{(}{)}{%
    #1\nonscript\medspace\delimsize\vert\nonscript\medspace\mathopen{}#2%
}



\begin{document}

Text before.
\begin{gather*}
    \begin{split}
        P\innerprod{\omega_{k}}{x} \approx \widehat{y_k}(x)
            = \frac{\exp(w^{T}_{k}x')}{\sum^{q}_{j=1}\exp(w^{T}_{j}x')}
        \qquad
        &\text{where} \quad x' = [1, x_1, x_2,\dots,x_p]^T  \\ 
        &\text{with} \quad 0 \leq \widehat{y_k}(x) \leq 1  \\
        &\text{and} \quad \sum^{q}_{k=1} \widehat{y_k}(x) = 1
    \end{split}
\end{gather*}
Text after.

A few examples of the use of \verb|\innerprod|:
\begin{align*}
    (a\mid b) &&
    \innerprod{a}{b} &&
    \innerprod[\Bigg]{a}{b} &&
    \innerprod*{\frac{a}{b}}{\frac{c}{d}}
\end{align*}

\end{document}

This is the output:

Answer 2

I propose one of these solutions, with the alignat environment:

\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}

\begin{document}

\begin{alignat*}{2}
  P(\omega_{k}|x) & \approx \widehat{y_k}(x) & & = \frac{\exp(w^{T}_{k}x')}{\sum^{q}_{j=1}\exp(w^{T}_{j}x')}
  \\[1ex]
                  & \text{where} & & \, x' = [1, x₁, x₂,...,x_p]^T \\[-1ex]
                  & \text{with} & & \, 0 \leq \widehat{y_k}(x) \leq 1 \quad \text{and} \quad \sum^{q}_{k=1} \widehat{y_k}(x) = 1
\end{alignat*}
\vskip1cm
\begin{alignat*}{2}
    & & & P(\omega_{k}|x) \approx \widehat{y_k}(x) = \frac{\exp(w^{T}_{k}x')}{\sum^{q}_{j=1}\exp(w^{T}_{j}x')}
  \\[1ex]
    & \text{where}\quad & & x' = [1, x₁, x₂,...,x_p]^T \\[-1ex]
    & \text{with} & & 0 \leq \widehat{y_k}(x) \leq 1 \quad \text{and} \quad \sum^{q}_{k=1} \widehat{y_k}(x) = 1
\end{alignat*}

\end{document}