How to align group of mathematical expressions to the left?

Question

Here are a group of mathematical expressions:

$$arg\ \underset{\theta}{max} \underset{n}{\prod}P(Y_n|\theta)$$
$$=arg\ \underset{\theta}{max} \underset{n}{\prod}\theta^{Y_n}(1-\theta)^{1-Y_n}$$
$$=arg\ \underset{\theta}{max} \sum log\theta^{Y_n}(1-\theta)^{1-Y_n}$$
$$=arg\ \underset{\theta}{max} \sum[Y_n log\theta + (1-Y_n)log(1-\theta)] $$
Optimizing problem:
$$=-arg\ \underset{\theta}{min} \sum[Y_n log\theta + (1-Y_n)log(1-\theta)] $$

I am trying to align them to the left. I tried putting them inside %\begin{align*} ... % \end{align*} without $$ signs. But no luck.

Please describe your problem better, which code (MWE) did you tried, and what is still the problem, for example mark it in the screenshot added to your question ... — Mensch, Jun 03 '17 at 18:08

cmhughes · Accepted Answer · 2017-06-04T08:30:00.423

Without a complete MWE, it's difficult to know what you're after, but I assume it's something like this:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
    \arg\ \underset{\theta}{\max} \underset{n}{\prod}P(Y_n|\theta) & =\arg\ \underset{\theta}{\max} \underset{n}{\prod}\theta^{Y_n}(1-\theta)^{1-Y_n} \\
                                                                   & =\arg\ \underset{\theta}{\max} \sum \log\theta^{Y_n}(1-\theta)^{1-Y_n}           \\
                                                                   & =\arg\ \underset{\theta}{\max} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]      \\
    \intertext{Optimizing problem:}
                                                                   & =-\arg\ \underset{\theta}{\min} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]     \\
\end{align*}
alternatively:
\begin{flalign*}
    & \arg\ \underset{\theta}{\max} \underset{n}{\prod}P(Y_n|\theta) \\
    & =\arg\ \underset{\theta}{\max} \underset{n}{\prod}\theta^{Y_n}(1-\theta)^{1-Y_n} \\
    & =\arg\ \underset{\theta}{\max} \sum \log\theta^{Y_n}(1-\theta)^{1-Y_n}          \\
    & =\arg\ \underset{\theta}{\max} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]     \\
    \intertext{Optimizing problem:}
    & =-\arg\ \underset{\theta}{\min} \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)]    \\
\end{flalign*}
\end{document}

alternatively, perhaps you'd like flalign:

@Dipto_Das if you provide a screenshot of your desired output, it'd be most helpful — cmhughes, Jun 03 '17 at 18:05

Mico · Answer 2 · 2017-06-03T18:13:05.460

1

The following may be what you're looking for. Note the use of \arg, \max, \min, and \log to generate upright math-operator expressions. I've also replaced the two instances of \underset{n}{\prod} with \prod_n.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
& \arg\max_\theta \prod_n P(Y_n\mid\theta)\\
&=\arg\max_\theta \prod_n \theta^{Y_n}(1-\theta)^{1-Y_n}\\
&=\arg\max_\theta \sum \log\bigl(\theta^{Y_n}(1-\theta)^{1-Y_n}\bigr)\\
&=\arg\max_\theta \sum [Y_n \log\theta + (1-Y_n)\log(1-\theta)]\\
\intertext{Optimizing problem:}
&-\arg\min_\theta \sum[Y_n \log\theta + (1-Y_n)\log(1-\theta)] 
\end{align*}
\end{document}

edited Jun 03 '17 at 18:13

answered Jun 03 '17 at 18:07

Mico

506,678

Your code does what I want, but it places everything in the center of the page. I want them all to start from the left margin. How can I do that? – Dipto_Das Jun 03 '17 at 18:44
@Dipto_Das - You could (a) switch from an align* environment to an flalign* environment and (b) add a & marker at the end of one of the math lines (but before the double line-break directive). E.g., change \prod_n P(Y_n\mid\theta) to \prod_n P(Y_n\mid\theta)&. – Mico Jun 03 '17 at 19:07

How to align group of mathematical expressions to the left?

2 Answers2