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<div class="section" id="Demo-Gaussian-Mechanism-Confidence-Interval">
<h1>Demo Gaussian Mechanism Confidence Interval<a class="headerlink" href="#Demo-Gaussian-Mechanism-Confidence-Interval" title="Permalink to this headline">¶</a></h1>
<div class="nbinput docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
</pre></div>
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<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
<span></span><span class="kn">from</span> <span class="nn">eeprivacy</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">gaussian_mechanism</span><span class="p">,</span>
<span class="n">gaussian_mechanism_confidence_interval</span><span class="p">,</span>
<span class="n">gaussian_mechanism_epsilon_for_confidence_interval</span><span class="p">,</span>
<span class="p">)</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib</span> <span class="k">as</span> <span class="nn">mpl</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">1234</span><span class="p">)</span> <span class="c1"># Fix seed for deterministic documentation</span>
<span class="n">mpl</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s2">"seaborn-white"</span><span class="p">)</span>
<span class="n">MD</span> <span class="o">=</span> <span class="mi">20</span>
<span class="n">LG</span> <span class="o">=</span> <span class="mi">24</span>
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="o">.</span><span class="n">update</span><span class="p">({</span>
<span class="s2">"figure.figsize"</span><span class="p">:</span> <span class="p">[</span><span class="mi">25</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span>
<span class="s2">"legend.fontsize"</span><span class="p">:</span> <span class="n">MD</span><span class="p">,</span>
<span class="s2">"axes.labelsize"</span><span class="p">:</span> <span class="n">LG</span><span class="p">,</span>
<span class="s2">"axes.titlesize"</span><span class="p">:</span> <span class="n">LG</span><span class="p">,</span>
<span class="s2">"xtick.labelsize"</span><span class="p">:</span> <span class="n">LG</span><span class="p">,</span>
<span class="s2">"ytick.labelsize"</span><span class="p">:</span> <span class="n">LG</span><span class="p">,</span>
<span class="p">})</span>
<span class="c1"># Exact</span>
<span class="n">ci</span> <span class="o">=</span> <span class="n">gaussian_mechanism_confidence_interval</span><span class="p">(</span>
<span class="n">epsilon</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">sensitivity</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">confidence</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">delta</span><span class="o">=</span><span class="mf">1e-12</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Exact CI: </span><span class="si">{</span><span class="n">ci</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="c1"># Stochastic</span>
<span class="n">trials</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000</span><span class="p">):</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">gaussian_mechanism</span><span class="p">(</span>
<span class="n">values</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">1000</span><span class="p">),</span>
<span class="n">epsilon</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
<span class="n">sensitivity</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
<span class="n">delta</span><span class="o">=</span><span class="mf">1e-12</span>
<span class="p">)</span>
<span class="n">trials</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">quantile</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="mf">0.975</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">trials</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"CI from stochastic trial"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"CI"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"Count"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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Exact CI: 14.628781668617956
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<span></span><span class="c1"># Now the reverse</span>
<span class="n">epsilon</span> <span class="o">=</span> <span class="n">gaussian_mechanism_epsilon_for_confidence_interval</span><span class="p">(</span>
<span class="n">target_ci</span><span class="o">=</span><span class="mf">14.62</span><span class="p">,</span>
<span class="n">sensitivity</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">confidence</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span>
<span class="n">delta</span><span class="o">=</span><span class="mf">1e-12</span>
<span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">epsilon</span><span class="p">)</span>
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1.0006006613281777
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<span></span><span class="n">trials</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">):</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">private_mean_with_laplace</span><span class="p">(</span><span class="n">values</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">epsilon</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">lower_bound</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">upper_bound</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">trials</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">trials</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">trials</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">laplace</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000</span><span class="p">):</span>
<span class="n">A</span> <span class="o">=</span> <span class="n">private_mean_with_laplace</span><span class="p">(</span><span class="n">values</span><span class="o">=</span><span class="n">values</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">lower_bound</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">upper_bound</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="n">trials</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">values</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">values</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">trials</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">trials</span><span class="p">))</span>
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<span class="ansi-red-fg">---------------------------------------------------------------------------</span>
<span class="ansi-red-fg">NameError</span> Traceback (most recent call last)
<span class="ansi-green-fg"><ipython-input-3-16c6f3877e5f></span> in <span class="ansi-cyan-fg"><module></span>
<span class="ansi-green-intense-fg ansi-bold"> 1</span> trials <span class="ansi-blue-fg">=</span> <span class="ansi-blue-fg">[</span><span class="ansi-blue-fg">]</span>
<span class="ansi-green-intense-fg ansi-bold"> 2</span> <span class="ansi-green-fg">for</span> t <span class="ansi-green-fg">in</span> range<span class="ansi-blue-fg">(</span><span class="ansi-cyan-fg">20</span><span class="ansi-blue-fg">)</span><span class="ansi-blue-fg">:</span>
<span class="ansi-green-fg">----> 3</span><span class="ansi-red-fg"> </span>A <span class="ansi-blue-fg">=</span> private_mean_with_laplace<span class="ansi-blue-fg">(</span>values<span class="ansi-blue-fg">=</span><span class="ansi-blue-fg">[</span><span class="ansi-cyan-fg">0</span><span class="ansi-blue-fg">,</span> <span class="ansi-cyan-fg">0</span><span class="ansi-blue-fg">,</span> <span class="ansi-cyan-fg">0</span><span class="ansi-blue-fg">]</span><span class="ansi-blue-fg">,</span> epsilon<span class="ansi-blue-fg">=</span><span class="ansi-cyan-fg">1.0</span><span class="ansi-blue-fg">,</span> lower_bound<span class="ansi-blue-fg">=</span><span class="ansi-cyan-fg">0</span><span class="ansi-blue-fg">,</span> upper_bound<span class="ansi-blue-fg">=</span><span class="ansi-cyan-fg">1</span><span class="ansi-blue-fg">)</span>
<span class="ansi-green-intense-fg ansi-bold"> 4</span> trials<span class="ansi-blue-fg">.</span>append<span class="ansi-blue-fg">(</span>A<span class="ansi-blue-fg">)</span>
<span class="ansi-green-intense-fg ansi-bold"> 5</span>
<span class="ansi-red-fg">NameError</span>: name 'private_mean_with_laplace' is not defined
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