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<p class="caption"><span class="caption-text">Core Library:</span></p>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">eeprivacy</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#algorithm-design">Algorithm Design</a></li>
<li class="toctree-l2"><a class="reference internal" href="#noise-functions">Noise Functions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="laplace-mechanism-basics.html">Laplace Mechanism Basics</a></li>
<li class="toctree-l1"><a class="reference internal" href="gaussian-mechanism-basics.html">Gaussian Mechanism Basics</a></li>
<li class="toctree-l1"><a class="reference internal" href="stochastic-testing.html">Stochastically Testing Privacy Mechanisms</a></li>
<li class="toctree-l1"><a class="reference internal" href="clamped-mean-bounds.html">Computing Bounds for Clamped Means</a></li>
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<div class="section" id="module-eeprivacy">
<span id="eeprivacy"></span><h1>eeprivacy<a class="headerlink" href="#module-eeprivacy" title="Permalink to this headline">¶</a></h1>
<div class="section" id="algorithm-design">
<h2>Algorithm Design<a class="headerlink" href="#algorithm-design" title="Permalink to this headline">¶</a></h2>
<p>The following functions help analysts in choosing parameters for private analytics, exploring the trade-offs of different choices of privacy parameters on accuracy/utility.</p>
<blockquote>
<div><dl class="py function">
<dt id="eeprivacy.laplace_mechanism_sensitivity_for_mean">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">laplace_mechanism_sensitivity_for_mean</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">population_size</span><span class="p">:</span> <span class="n">int</span></em>, <em class="sig-param"><span class="n">rows_per_individual</span><span class="p">:</span> <span class="n">int</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.laplace_mechanism_sensitivity_for_mean" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the sensitivity for means computed with the Laplace Mechanism.</p>
<p>Supports single value means and vector-valued mean (where each individual
contributes more than one row to the output).</p>
<p>The sensitivity is scaled to the L1 norm of the vector.</p>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.laplace_mechanism_epsilon_for_confidence_interval">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">laplace_mechanism_epsilon_for_confidence_interval</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">target_ci</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.laplace_mechanism_epsilon_for_confidence_interval" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the ε for the Laplace Mechanism that will produce outputs
+/-<cite>target_ci</cite> at <cite>confidence</cite> for queries with <cite>sensitivity</cite>.</p>
<p>For the default <cite>confidence</cite> = 0.95 and <cite>target_ci</cite> = 5, the distribution
of outputs for the returned ε would be the following:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> .25% │ █ │ .25%
◀──────│ █ │──────▶
│ █ │
│ ███ │
│ ███ │
│ ███ │
│ ███ │
│ ███ │
│ █████ │
│ ███████ │
│ █████████ │
│█████████████│
███│█████████████│███
─────┼──────┬──────┼────
│ │ │
True
-5 Count 5
</pre></div>
</div>
<p class="rubric">Example</p>
<p>Find ε for counting queries that should be within +/-5 of the true count
at 99% confidence.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">compute_laplace_epsilon</span><span class="p">(</span><span class="n">target_ci</span><span class="o">=</span><span class="mi">5</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">0.99</span><span class="p">)</span>
<span class="go">0.64</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.laplace_mechanism_confidence_interval">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">laplace_mechanism_confidence_interval</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.laplace_mechanism_confidence_interval" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the confidence interval for the Laplace Mechanism at a given
<code class="docutils literal notranslate"><span class="pre">epsilon</span></code> and <code class="docutils literal notranslate"><span class="pre">sensitivity</span></code>.</p>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.gaussian_mechanism_sensitivity_for_mean">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">gaussian_mechanism_sensitivity_for_mean</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">population_size</span><span class="p">:</span> <span class="n">int</span></em>, <em class="sig-param"><span class="n">rows_per_individual</span><span class="p">:</span> <span class="n">int</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.gaussian_mechanism_sensitivity_for_mean" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the sensitivity for means computed with the Gaussian Mechanism.</p>
<p>Supports single value means and vector-valued mean (where each individual
contributes more than one row to the output).</p>
<p>The sensitivity is scaled to the L2 norm of the vector.</p>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.gaussian_mechanism_epsilon_for_confidence_interval">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">gaussian_mechanism_epsilon_for_confidence_interval</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">target_ci</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">delta</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.gaussian_mechanism_epsilon_for_confidence_interval" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the ε for the Gaussian Mechanism that will produce outputs
+/-<cite>target_ci</cite> at <cite>confidence</cite> for queries with <cite>sensitivity</cite> and <cite>delta</cite>.</p>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.gaussian_mechanism_confidence_interval">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">gaussian_mechanism_confidence_interval</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">delta</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.gaussian_mechanism_confidence_interval" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the confidence interval for the Laplace Mechanism at a given
<code class="docutils literal notranslate"><span class="pre">epsilon</span></code>, <code class="docutils literal notranslate"><span class="pre">delta</span></code>, and <code class="docutils literal notranslate"><span class="pre">sensitivity</span></code>.</p>
</dd></dl>
</div></blockquote>
</div>
<div class="section" id="noise-functions">
<h2>Noise Functions<a class="headerlink" href="#noise-functions" title="Permalink to this headline">¶</a></h2>
<p>Noise functions implement core differential privacy functions.</p>
<blockquote>
<div><dl class="py function">
<dt id="eeprivacy.laplace_mechanism">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">laplace_mechanism</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">value</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.laplace_mechanism" title="Permalink to this definition">¶</a></dt>
<dd><p>Run the Laplace Mechanism, adding noise to <cite>value</cite> to realize differential
private at <cite>epsilon</cite> for the provided <cite>sensitivity</cite>.</p>
<p>If a list of <code class="docutils literal notranslate"><span class="pre">values</span></code> is provided, run the Laplace Mechanism multiple times,
once for each item in the list.</p>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.laplace_mechanism_vec">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">laplace_mechanism_vec</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em><span class="sig-paren">)</span> → List<span class="p">[</span>float<span class="p">]</span><a class="headerlink" href="#eeprivacy.laplace_mechanism_vec" title="Permalink to this definition">¶</a></dt>
<dd><p>Run the Laplace Mechanism, adding noise to <cite>values</cite> to realize differential
private at <cite>epsilon</cite> for the provided <cite>sensitivity</cite>.</p>
<p>A separate draw is performed for each element of <cite>values</cite>.</p>
<dl class="simple">
<dt>TODO: semantically, this should be like vector-valued Gaussian and scale to</dt><dd><p>L1 senstivity instead of doing a separate draw for each element.</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.gaussian_mechanism">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">gaussian_mechanism</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">value</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">delta</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.gaussian_mechanism" title="Permalink to this definition">¶</a></dt>
<dd><p>Run the Gaussian Mechanism, adding noise to <cite>value</cite> to realize differential
private at (<cite>epsilon</cite>, <cite>delta</cite>) for the provided <cite>sensitivity</cite>.</p>
<p>If a list of <code class="docutils literal notranslate"><span class="pre">values</span></code> is provided, run the Gaussian Mechanism multiple times,
once for each item in the list.</p>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.gaussian_mechanism_vec">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">gaussian_mechanism_vec</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">delta</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">None</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.gaussian_mechanism_vec" title="Permalink to this definition">¶</a></dt>
<dd><p>Run the Gaussian Mechanism, adding noise to <cite>values</cite> to realize differential
private at (<cite>epsilon</cite>, <cite>delta</cite>) for the provided <cite>sensitivity</cite>.</p>
<p>In constrast to the Gaussian Mechanism run N times, once for each value
in <cite>values</cite>, the <cite>vec</cite> form is for queries of vector-valued functions,
where each individual contributes multiple points to the output.</p>
</dd></dl>
</div></blockquote>
</div>
<div class="section" id="convenience-methods">
<h2>Convenience Methods<a class="headerlink" href="#convenience-methods" title="Permalink to this headline">¶</a></h2>
<p>Convenience methods compose noise functions into common analytics tasks like computing means and histograms.</p>
<blockquote>
<div><dl class="py function">
<dt id="eeprivacy.private_mean_with_laplace">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">private_mean_with_laplace</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">lower_bound</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">upper_bound</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → Tuple<span class="p">[</span>float<span class="p">, </span>float<span class="p">]</span><a class="headerlink" href="#eeprivacy.private_mean_with_laplace" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the mean of <cite>values</cite> privately using a clamped mean.</p>
<p>Implements Algorithm 2.3 from [Li et al] in Differential Privacy: From Theory to Practice</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>private mean and confidence interval for private mean</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>Tuple[float, float]</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.private_vec_sum_with_gaussian">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">private_vec_sum_with_gaussian</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">vectors</span><span class="p">:</span> <span class="n">List<span class="p">[</span>List<span class="p">[</span>float<span class="p">]</span><span class="p">]</span></span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">delta</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">lower_bound</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">upper_bound</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → Tuple<span class="p">[</span>List<span class="p">[</span>float<span class="p">]</span><span class="p">, </span>float<span class="p">]</span><a class="headerlink" href="#eeprivacy.private_vec_sum_with_gaussian" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the mean of vectors <cite>vectors</cite> privately using a clamped sum with the Gaussian
Mechanism.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>private vector sum
float:</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>List[float]</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.private_histogram_with_laplace">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">private_histogram_with_laplace</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span></em>, <em class="sig-param"><span class="n">bins</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span> <span class="o">=</span> <span class="default_value">None</span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">1.0</span></em>, <em class="sig-param"><span class="n">confidence</span><span class="p">:</span> <span class="n">float</span> <span class="o">=</span> <span class="default_value">0.95</span></em><span class="sig-paren">)</span> → Tuple<span class="p">[</span>List<span class="p">[</span>float<span class="p">]</span><span class="p">, </span>float<span class="p">]</span><a class="headerlink" href="#eeprivacy.private_histogram_with_laplace" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the histogram of <cite>values</cite> privately.</p>
<p>Values are clamped to the bound specified by <code class="docutils literal notranslate"><span class="pre">bins</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>values</strong> (<em>List</em><em>[</em><em>float</em><em>]</em>) – Values to bin into histogram</p></li>
<li><p><strong>bins</strong> (<em>List</em><em>[</em><em>float</em><em>]</em>) – Edges of bins for results. These must be specified up-front
otherwise information will be leaked by the choice of bins. <a class="reference external" href="https://desfontain.es/privacy/almost-differential-privacy.html">Read more</a></p></li>
<li><p><strong>epsilon</strong> (<em>float</em>) – privacy parameter</p></li>
<li><p><strong>sensitivity</strong> (<em>float</em>) – Defaults to one (assumes a counting query)</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Private count for each bin.
float: Confidence interval for each bin of the histogram</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>List[float]</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="eeprivacy.private_quantile">
<code class="sig-prename descclassname">eeprivacy.</code><code class="sig-name descname">private_quantile</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span></em>, <em class="sig-param"><span class="n">options</span><span class="p">:</span> <span class="n">List<span class="p">[</span>float<span class="p">]</span></span></em>, <em class="sig-param"><span class="n">quantile</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">epsilon</span><span class="p">:</span> <span class="n">float</span></em>, <em class="sig-param"><span class="n">sensitivity</span><span class="p">:</span> <span class="n">float</span></em><span class="sig-paren">)</span> → float<a class="headerlink" href="#eeprivacy.private_quantile" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the quantile of a list of values privately.</p>
<p>Implemented using Report Noisy Max (Claim 3.9) of Dwork and Roth.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>values</strong> (<em>List</em><em>[</em><em>float</em><em>]</em>) – Dataset</p></li>
<li><p><strong>options</strong> (<em>List</em><em>[</em><em>float</em><em>]</em>) – List of possible outputs</p></li>
<li><p><strong>quantile</strong> (<em>float</em>) – Quantile to return (between 0 and 1)</p></li>
<li><p><strong>epsilon</strong> (<em>float</em>) – Privacy parameter</p></li>
<li><p><strong>sensitivity</strong> (<em>float</em>) – Normally 1, unless an individual can contribute
multiple points to the dataset.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</div></blockquote>
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