31:T90e,chart = { const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]); svg.append("g") .call(xAxis); svg.append("g") .call(yAxis); svg.append("path") .datum(ftrlData) .attr("fill", "none") .attr("stroke", "steelblue") .attr("stroke-width", 1.5) .attr("stroke-linejoin", "round") .attr("stroke-linecap", "round") .attr("d", line); svg.append("path") .datum(sgdData) .attr("fill", "none") .attr("stroke", "maroon") .attr("stroke-width", 1.5) .attr("stroke-linejoin", "round") .attr("stroke-linecap", "round") .attr("d", line); const lastFTRLVal = sweepMin < sweepMax ? ftrlData[ftrlData.length - 1]: ftrlData[0]; svg.append("text") .datum({x: lastFTRLVal.x, y: lastFTRLVal.y, name: 'DP-FTRL'}) .attr("fill", "steelblue") .attr("x", d => x(d.x) + 5) .attr("y", d => y(d.y)) .attr("dy", "0.35em") .style("font", "13px sans-serif") .text(d => d.name); const lastSGDVal = sweepMin < sweepMax ? sgdData[sgdData.length - 1]: sgdData[0]; svg.append("text") .datum({x: lastSGDVal.x, y: lastSGDVal.y, name: 'DP-SGD'}) .attr("fill", "maroon") .attr("x", d => x(d.x) + 5) .attr("y", d => y(d.y)) .attr("dy", "0.35em") .style("font", "13px sans-serif") .text(d => d.name); if(tooltipOver === 'DP-FTRL'){ const ftrlTooltip = svg.append("g"); svg.on("touchmove mousemove", function(event) { const coords = d3.pointer(event, this)[0]; const {x: xVal, y: yVal} = bisect(ftrlData)(coords); ftrlTooltip .attr("transform", `translate(${x(xVal)},${y(yVal)})`) .call(callout, `${yVal}\n${xVal}`); }); svg.on("touchend mouseleave", () => ftrlTooltip.call(callout, null)); } else if(tooltipOver === 'DP-SGD'){ const sgdTooltip = svg.append("g"); svg.on("touchmove mousemove", function(event) { const coords = d3.pointer(event, this)[0]; const {x: xVal, y: yVal} = bisect(sgdData)(coords); sgdTooltip .attr("transform", `translate(${x(xVal)},${y(yVal)})`) .call(callout, `${yVal}\n${xVal}`); }); svg.on("touchend mouseleave", () => sgdTooltip.call(callout, null)); } return svg.node(); }32:T4df,/* """ Sourced from https://github.com/google-research/DP-FTRL/blob/main/privacy.py """ def convert_gaussian_renyi_to_dp(sigma, delta, verbose=True): """ Convert from RDP to DP for a Gaussian mechanism. :param sigma: the algorithm guarantees (alpha, alpha/(2*sigma^2))-RDP :param delta: target DP delta :param verbose: whether to print message :return: the DP epsilon """ alphas = np.arange(1, 200, 0.1)[1:] epss = alphas / 2 / sigma**2 - (np.log(delta*(alphas - 1)) - alphas * np.log(1 - 1/alphas)) / (alphas - 1) idx = np.nanargmin(epss) if verbose and idx == len(alphas) - 1: print('The best alpha is the last one. Consider increasing the range of alpha.') eps = epss[idx] return eps */ function convertRenyiToDP({alphas, rdps, targetDelta}){ const alphas_minus_1 = math.subtract(alphas, 1); const alphas_minus_1_by_alpha = math.dotDivide(alphas_minus_1, alphas); const epsilons = math.subtract( rdps, math.dotDivide(math.subtract(math.log(math.dotMultiply(targetDelta, alphas_minus_1)), math.dotMultiply(alphas, math.log(alphas_minus_1_by_alpha))), alphas_minus_1)); return math.min(epsilons); } 33:T470,/* """ Adapted from https://github.com/tensorflow/privacy/blob/master/tensorflow_privacy/privacy/analysis/rdp_accountant.py """ def _log_sub(logx, logy): """Subtract two numbers in the log space. Answer must be non-negative.""" if logx < logy: raise ValueError("The result of subtraction must be non-negative.") if logy == -np.inf: # subtracting 0 return logx if logx == logy: return -np.inf # 0 is represented as -np.inf in the log space. try: # Use exp(x) - exp(y) = (exp(x - y) - 1) * exp(y). return math.log(math.expm1(logx - logy)) + logy # expm1(x) = exp(x) - 1 except OverflowError: return logx */ function _log_sub(logx, logy){ // Subtract two numbers in the log space. Answer must be non-negative. if(logx < logy){ throw 'The result of subtraction must be non-negative.'; } if(logy == -math.Infinity){ // subtracting 0 return logx; } if(logx == logy){ return -math.Infinity; // 0 is represented as -np.inf in the log space. } // Use exp(x) - exp(y) = (exp(x - y) - 1) * exp(y). return math.log(math.expm1(logx - logy)) + logy; // expm1(x) = exp(x) - 1 }34:T526,/* """ Adapted from https://github.com/tensorflow/privacy/blob/master/tensorflow_privacy/privacy/analysis/rdp_accountant.py """ def _log_erfc(x): """Compute log(erfc(x)) with high accuracy for large x.""" try: return math.log(2) + special.log_ndtr(-x * 2**.5) except NameError: # If log_ndtr is not available, approximate as follows: r = special.erfc(x) if r == 0.0: # Using the Laurent series at infinity for the tail of the erfc function: # erfc(x) ~ exp(-x^2-.5/x^2+.625/x^4)/(x*pi^.5) # To verify in Mathematica: # Series[Log[Erfc[x]] + Log[x] + Log[Pi]/2 + x^2, {x, Infinity, 6}] return (-math.log(math.pi) / 2 - math.log(x) - x**2 - .5 * x**-2 + .625 * x**-4 - 37. / 24. * x**-6 + 353. / 64. * x**-8) else: return math.log(r) */ function _log_erfc(x){ let r = stdlib.base.erfc(x); if(r == 0.0) { // Using the Laurent series at infinity for the tail of the erfc function: // erfc(x) ~ exp(-x^2-.5/x^2+.625/x^4)/(x*pi^.5) // To verify in Mathematica: // Series[Log[Erfc[x]] + Log[x] + Log[Pi]/2 + x^2, {x, Infinity, 6}] return (-math.log(math.pi) / 2 - math.log(x) - x**2 - .5 * x**-2 + .625 * x**-4 - 37. / 24. * x**-6 + 353. / 64. * x**-8) } else { return math.log(r); } }35:T100e,/* """ Adapted from https://github.com/tensorflow/privacy/blob/master/tensorflow_privacy/privacy/analysis/rdp_accountant.py """ def _compute_log_a_int(q, sigma, alpha): """Compute log(A_alpha) for integer alpha. 0 < q < 1.""" assert isinstance(alpha, six.integer_types) # Initialize with 0 in the log space. log_a = -np.inf for i in range(alpha + 1): log_coef_i = ( _log_comb(alpha, i) + i * math.log(q) + (alpha - i) * math.log(1 - q)) s = log_coef_i + (i * i - i) / (2 * (sigma**2)) log_a = _log_add(log_a, s) return float(log_a) def _compute_log_a_frac(q, sigma, alpha): """Compute log(A_alpha) for fractional alpha. 0 < q < 1.""" # The two parts of A_alpha, integrals over (-inf,z0] and [z0, +inf), are # initialized to 0 in the log space: log_a0, log_a1 = -np.inf, -np.inf i = 0 z0 = sigma**2 * math.log(1 / q - 1) + .5 while True: # do ... until loop coef = special.binom(alpha, i) log_coef = math.log(abs(coef)) j = alpha - i log_t0 = log_coef + i * math.log(q) + j * math.log(1 - q) log_t1 = log_coef + j * math.log(q) + i * math.log(1 - q) log_e0 = math.log(.5) + _log_erfc((i - z0) / (math.sqrt(2) * sigma)) log_e1 = math.log(.5) + _log_erfc((z0 - j) / (math.sqrt(2) * sigma)) log_s0 = log_t0 + (i * i - i) / (2 * (sigma**2)) + log_e0 log_s1 = log_t1 + (j * j - j) / (2 * (sigma**2)) + log_e1 if coef > 0: log_a0 = _log_add(log_a0, log_s0) log_a1 = _log_add(log_a1, log_s1) else: log_a0 = _log_sub(log_a0, log_s0) log_a1 = _log_sub(log_a1, log_s1) i += 1 if max(log_s0, log_s1) < -30: break return _log_add(log_a0, log_a1) def _compute_log_a(q, sigma, alpha): """Compute log(A_alpha) for any positive finite alpha.""" if float(alpha).is_integer(): return _compute_log_a_int(q, sigma, int(alpha)) else: return _compute_log_a_frac(q, sigma, alpha) */ function computeLogA({samplingProbability, noiseMultiplier, alpha}){ function computeLogAInt({samplingProbability, noiseMultiplier, alpha}){ // Compute log(A_alpha) for integer alpha. 0 < q < 1. let sigma = noiseMultiplier; let q = samplingProbability; // Initialize with 0 in the log space. let log_a = -math.Infinity; for(let i = 0; i <= alpha; i++){ let log_coef_i = ( _log_comb(alpha, i) + i * math.log(q) + (alpha - i) * math.log(1 - q)); let s = log_coef_i + (i * i - i) / (2 * (sigma**2)); log_a = _log_add(log_a, s); } return log_a; } function computeLogAFrac({samplingProbability, noiseMultiplier, alpha}){ // Compute log(A_alpha) for fractional alpha. // The two parts of A_alpha, integrals over (-inf,z0] and [z0, +inf), are // initialized to 0 in the log space: let [log_a0, log_a1] = [-math.Infinity, -math.Infinity]; let i = 0; let sigma = noiseMultiplier; let q = samplingProbability; let z0 = sigma**2 * math.log(1 / q - 1) + .5; while(true){ // do ... until loop let [log_coef, sign] = log_abs_binom(alpha, i); let j = alpha - i; let log_t0 = log_coef + i * math.log(q) + j * math.log(1 - q); let log_t1 = log_coef + j * math.log(q) + i * math.log(1 - q); let log_e0 = math.log(.5) + _log_erfc((i - z0) / (math.sqrt(2) * sigma)); let log_e1 = math.log(.5) + _log_erfc((z0 - j) / (math.sqrt(2) * sigma)); let log_s0 = log_t0 + (i * i - i) / (2 * (sigma**2)) + log_e0; let log_s1 = log_t1 + (j * j - j) / (2 * (sigma**2)) + log_e1; if(sign > 0){ log_a0 = _log_add(log_a0, log_s0) log_a1 = _log_add(log_a1, log_s1) } else { log_a0 = _log_sub(log_a0, log_s0) log_a1 = _log_sub(log_a1, log_s1) } i += 1 if(math.max(log_s0, log_s1) < -30){ break; } if(i == 60){ break; } } return _log_add(log_a0, log_a1); } if(Number.isInteger(alpha)){ return computeLogAInt({samplingProbability, noiseMultiplier, alpha}); } else { return computeLogAFrac({samplingProbability, noiseMultiplier, alpha}); } }36:T5f3,/* """ Adapted from https://github.com/google-research/DP-FTRL/blob/main/privacy.py """ def compute_epsilon_tree(restart, epochs, num_batches, noise, delta, verbose=True): """ Compute epsilon value for DP-FTRL. :param restart: whether to restart the tree after each epoch :param epochs: number of epochs :param num_batches: number of batches per epoch :param noise: noise multiplier for each step :param delta: target DP delta :param verbose: whether to print message :return: the DP epsilon for DP-FTRL """ if noise < 1e-20: return float('inf') if not restart: num_batches *= epochs log_num_batches = np.ceil(np.log2(num_batches)) eps = convert_gaussian_renyi_to_dp(noise / math.sqrt(log_num_batches * epochs), delta, verbose) return epsilonValues */ function computeFTRLepsilon({numSamples, batchSize, ftrlNoiseMultiplier, numTrainingSteps, targetDelta, resetTree}){ const numEpochs = math.ceil((numTrainingSteps * batchSize) / numSamples); const numBatchesPerEpoch = math.ceil(numSamples / batchSize); let factor = resetTree ? numBatchesPerEpoch : numBatchesPerEpoch * numEpochs; const logFactor = math.max(1, math.ceil(math.log2(factor))); const sigma = ftrlNoiseMultiplier / math.sqrt(logFactor * numEpochs); const alphas = math.range(1.1, 200, 0.1); const rdps = math.dotDivide(alphas, 2 * sigma**2); return convertRenyiToDP({alphas, rdps, targetDelta}); }37:[] 2f:{"title":"Interactive Differential Privacy Accountants","cells":[{"id":0,"value":"md`# Interactive Differential Privacy Accountants`","pinned":false,"hidden":false,"mode":"ojs"},{"id":622,"value":"md`Select the quantity to sweep over, and see how the resulting privacy parameters change!`","pinned":false,"hidden":false,"mode":"ojs"},{"id":26,"value":"viewof sweepOverName = Inputs.radio(datasetParameterNames,\n {value: numSamplesLabel, label: html`Sweep Over?`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":382,"value":"viewof sweepMin = Inputs.range(sweepOverInfo.range, {value: sweepOverInfo.defaultMin,\n label: `${sweepOverName} (min)`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":384,"value":"viewof sweepMax = Inputs.range(sweepOverInfo.range, {value: sweepOverInfo.defaultMax,\n label: `${sweepOverName} (max)`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":632,"value":"md`---`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":2,"value":"viewof numSamples = Inputs.range([1, 10_000_00], {step: 1, value: 5_000_000, label: numSamplesLabel})","pinned":false,"hidden":false,"mode":"ojs"},{"id":10,"value":"viewof batchSize = Inputs.range([1, 10_000_000], {step: 1, value: 1000, label: batchSizeLabel})","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"viewof ftrlNoiseMultiplier = Inputs.range([0.01, 100], {transform: Math.log,\n format: x => x.toFixed(2),\n label: `${ftrlNoiseMultiplierLabel}`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1005,"value":"viewof sgdNoiseMultiplier = Inputs.range([0.01, 10], {transform: Math.log,\n format: x => x.toFixed(2),\n label: `${sgdNoiseMultiplierLabel}`})","pinned":false,"hidden":false,"mode":"ojs"},{"id":186,"value":"viewof numTrainingSteps = Inputs.range([1, 10_000_000],\n {step: 1, value: 5_000_000, label: numTrainingStepsLabel})","pinned":false,"hidden":false,"mode":"ojs"},{"id":218,"value":"viewof targetDelta = Inputs.range([1e-8, 1e-4], {transform: Math.log,\n label: targetDeltaLabel,\n value: 1e-5,\n format: x => x.toExponential(2)})","pinned":false,"hidden":false,"mode":"ojs"},{"id":542,"value":"viewof resetTree =\n Inputs.radio([true, false], {label: html`

Reset Tree After Every Epoch in DP-FTRL?

`,\n value: true,\n format: (x) => x ? 'Yes': 'No'});","pinned":false,"hidden":false,"mode":"ojs"},{"id":605,"value":"viewof yScale =\n Inputs.radio(['linear', 'log', 'sqrt'],\n {label: 'y-axis Scale',\n value: 'linear'});","pinned":false,"hidden":false,"mode":"ojs"},{"id":1032,"value":"viewof tooltipOver =\n Inputs.radio(['DP-FTRL', 'DP-SGD'],\n {label: 'Tooltip on Hover',\n value: 'DP-FTRL'});","pinned":false,"hidden":false,"mode":"ojs"},{"id":266,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":322,"value":"md`## Plotting Helpers`","pinned":false,"hidden":false,"mode":"ojs"},{"id":462,"value":"function showSliderCheck(){\n const label = d3.select(this).select('label');\n if(label == null){\n return false;\n }\n return label.text() === sweepOverName;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":394,"value":"sweepOverInfo = {\n switch(sweepOverName){\n case numSamplesLabel:\n return {\n range: [1, 10_000_000],\n defaultMin: 100_000,\n defaultMax: 1_000_000,\n };\n case batchSizeLabel:\n return {\n range: [1, 50_000],\n defaultMin: 1_000,\n defaultMax: 10_000,\n }\n case ftrlNoiseMultiplierLabel:\n return {\n range: [0.01, 10],\n defaultMin: 0.1,\n defaultMax: 1,\n }\n case sgdNoiseMultiplierLabel:\n return {\n range: [0.01, 10],\n defaultMin: 0.1,\n defaultMax: 1,\n }\n case numTrainingStepsLabel:\n return {\n range: [1, 10_000_000],\n defaultMin: 1_000,\n defaultMax: 10_000,\n }\n case targetDeltaLabel:\n return {\n range: [1e-8, 1e-4],\n defaultMin: 1e-6,\n defaultMax: 1e-5,\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":412,"value":"function isSweptOver(label){\n if(label === sweepOverName){\n console.log(d3.select(this));\n return true;\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":459,"value":"showSliders = { \n const forms = d3.selectAll('form');\n forms.select('div')\n .selectAll('input')\n .property('disabled', false);\n\n forms\n .select('label')\n .style('color', '');\n \n const filteredForms = forms.filter(showSliderCheck);\n filteredForms\n .select('label')\n .style('color', 'gray');\n\n filteredForms\n .select('div')\n .selectAll('input')\n .property('disabled', true);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":268,"value":"ftrlData = FTRLepsilonValues.map((epsilon, index) => ({x: sweepValues[index], y: epsilon}));","pinned":false,"hidden":false,"mode":"ojs"},{"id":979,"value":"sgdData = SGDepsilonValues.map((epsilon, index) => ({x: sweepValues[index], y: epsilon}));","pinned":false,"hidden":false,"mode":"ojs"},{"id":977,"value":"allData = ftrlData.concat(sgdData);","pinned":false,"hidden":false,"mode":"ojs"},{"id":295,"value":"line = d3.line()\n .x(d => x(d.x))\n .y(d => y(d.y))","pinned":false,"hidden":false,"mode":"ojs"},{"id":270,"value":"margin = ({top: 20, right: 80, bottom: 60, left: 80})","pinned":false,"hidden":false,"mode":"ojs"},{"id":272,"value":"height = 500","pinned":false,"hidden":false,"mode":"ojs"},{"id":279,"value":"x = d3.scaleLinear()\n .domain(d3.extent(sweepValues))\n .range([margin.left, width - margin.right])","pinned":false,"hidden":false,"mode":"ojs"},{"id":275,"value":"xAxis = g => g\n .attr(\"transform\", `translate(0,${height - margin.bottom})`)\n .call(d3.axisBottom(x).ticks(width / 80).tickSizeOuter(0))\n .call(g => g.select(\".tick text\").clone()\n .attr(\"x\", width / 2 - margin.left)\n .attr(\"y\", 30)\n .attr(\"text-anchor\", \"middle\")\n .attr(\"font-size\", \"12px\")\n .attr(\"font-weight\", \"bold\")\n .text(sweepOverName))","pinned":false,"hidden":false,"mode":"ojs"},{"id":614,"value":"yScaleFn = {\n switch(yScale){\n case 'linear':\n return d3.scaleLinear();\n case 'log':\n return d3.scaleLog();\n case 'sqrt':\n return d3.scaleSqrt();\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":277,"value":"y = yScaleFn\n .domain([0.5 * d3.min(allData, d => d.y), 1.5 * d3.max(allData, d => d.y)]).nice()\n .range([height - margin.bottom, margin.top])","pinned":false,"hidden":false,"mode":"ojs"},{"id":274,"value":"yAxis = g => g\n .attr(\"transform\", `translate(${margin.left},0)`)\n .call(d3.axisLeft(y))\n .call(g => g.select(\".domain\").remove())\n .call(g => g.select(\".tick:last-of-type text\").clone()\n .attr(\"x\", 3)\n .attr(\"text-anchor\", \"start\")\n .attr(\"font-weight\", \"bold\")\n .text('DP Epsilon'))","pinned":false,"hidden":false,"mode":"ojs"},{"id":659,"value":"callout = (g, value) => {\n if (!value) return g.style(\"display\", \"none\");\n\n g.style(\"display\", null)\n .style(\"pointer-events\", \"none\")\n .style(\"font\", \"10px sans-serif\");\n\n const path = g.selectAll(\"path\")\n .data([null])\n .join(\"path\")\n .attr(\"fill\", \"white\")\n .attr(\"stroke\", \"black\");\n\n const text = g.selectAll(\"text\")\n .data([null])\n .join(\"text\")\n .call(text => text\n .selectAll(\"tspan\")\n .data((value + \"\").split(/\\n/))\n .join(\"tspan\")\n .attr(\"x\", 0)\n .attr(\"y\", (d, i) => `${i * 1.1}em`)\n .style(\"font-weight\", (_, i) => i ? null : \"bold\")\n .text(d => d));\n\n const {x, y, width: w, height: h} = text.node().getBBox();\n\n text.attr(\"transform\", `translate(${-w / 2},${15 - y})`);\n path.attr(\"d\", `M${-w / 2 - 10},5H-5l5,-5l5,5H${w / 2 + 10}v${h + 20}h-${w + 20}z`);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":667,"value":"function bisect(data){\n const bisector = d3.bisector(d => d.x).left;\n return mx => {\n const xVal = x.invert(mx);\n const index = bisector(data, xVal, 1);\n const a = data[index - 1];\n const b = data[index];\n return b && (xVal - a.x > b.x - xVal) ? b : a;\n };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":164,"value":"md`## Computation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":101,"value":"numSweepPoints = 20","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"sweepValues = math.range(sweepMin, sweepMax, (sweepMax - sweepMin) / numSweepPoints, true).toArray()","pinned":false,"hidden":false,"mode":"ojs"},{"id":117,"value":"datasetParameters = sweepValues.map((sweepVal) => {\n const datasetParametersCurr = {...datasetParametersBase};\n datasetParametersCurr[sweepOver] = sweepVal;\n return datasetParametersCurr;\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":179,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":742,"value":"/*\n\"\"\"\nAdapted from https://github.com/tensorflow/privacy/blob/master/tensorflow_privacy/privacy/analysis/rdp_accountant.py\n\"\"\"\ndef _log_add(logx, logy):\n \"\"\"Add two numbers in the log space.\"\"\"\n a, b = min(logx, logy), max(logx, logy)\n if a == -np.inf: # adding 0\n return b\n # Use exp(a) + exp(b) = (exp(a - b) + 1) * exp(b)\n return math.log1p(math.exp(a - b)) + b # log1p(x) = log(x + 1)\n*/\nfunction _log_add(logx, logy){\n // Add two numbers in the log space.\n const [a, b] = [math.min(logx, logy), math.max(logx, logy)];\n if(a == -math.Infinity){ // x is 0.\n return b\n }\n // Use exp(a) + exp(b) = (exp(a - b) + 1) * exp(b)\n return math.log1p(math.exp(a - b)) + b // log1p(x) = log(x + 1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":846,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":863,"value":"/*\n\"\"\"\nAdapted from https://github.com/tensorflow/privacy/blob/master/tensorflow_privacy/privacy/analysis/rdp_accountant.py\n\"\"\"\ndef _log_sub_sign(logx, logy):\n \"\"\"Returns log(exp(logx)-exp(logy)) and its sign.\"\"\"\n if logx > logy:\n s = True\n mag = logx + np.log(1 - np.exp(logy - logx))\n elif logx < logy:\n s = False\n mag = logy + np.log(1 - np.exp(logx - logy))\n else:\n s = True\n mag = -np.inf\n\n return s, mag\n*/\nfunction _log_sub_sign(logx, logy){\n // Returns log(exp(logx)-exp(logy)) and its sign.\n let s, mag;\n if(logx > logy){\n s = true;\n mag = logx + math.log(1 - math.exp(logy - logx));\n }\n else if(logx < logy){\n s = false;\n mag = logy + math.log(1 - math.exp(logx - logy));\n }\n else{\n s = true;\n mag = -math.Infinity;\n }\n return [s, mag];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":866,"value":"/*\n\"\"\"\nAdapted from https://github.com/tensorflow/privacy/blob/master/tensorflow_privacy/privacy/analysis/rdp_accountant.py\n\"\"\"\ndef _log_comb(n, k):\n return (special.gammaln(n + 1) -\n special.gammaln(k + 1) - special.gammaln(n - k + 1))\n*/\nfunction _log_comb(n, k){\n return (stdlib.base.gammaln(n + 1) -\n stdlib.base.gammaln(k + 1) - stdlib.base.gammaln(n - k + 1));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":877,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":923,"value":"function log_abs_binom(n, k){\n let sign = 1;\n let ans = 0;\n for(let m = n; m > n - k; --m){\n if(m < 0){\n sign = -sign;\n }\n ans += math.log(math.abs(m));\n }\n for(let r = k; r > 0; --r){\n ans -= math.log(math.abs(r));\n } \n return [ans, sign];\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":734,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":730,"value":"function computeOneStepRDP({samplingProbability, noiseMultiplier, alpha}){\n if(samplingProbability == 0){\n return 0;\n }\n if(samplingProbability == 1){\n return alpha / (2 * noiseMultiplier**2);\n }\n const logA = computeLogA({samplingProbability, noiseMultiplier, alpha});\n return math.dotDivide(logA,\n math.subtract(alpha, 1));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":727,"value":"function computeRDPs({samplingProbability, noiseMultiplier, numTrainingSteps, alphas}){\n const baseRDPs = alphas.map((alpha) => computeOneStepRDP({samplingProbability, noiseMultiplier, alpha}));\n return math.dotMultiply(baseRDPs, numTrainingSteps);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":200,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":177,"value":"FTRLepsilonValues = datasetParameters.map(computeFTRLepsilon);","pinned":false,"hidden":false,"mode":"ojs"},{"id":690,"value":"function computeSGDepsilon({numSamples, batchSize, sgdNoiseMultiplier,\n numTrainingSteps, targetDelta, resetTree}){\n const samplingProbability = batchSize / numSamples;\n const alphas = math.range(1.1, 3, 0.1);\n const rdps = computeRDPs({samplingProbability,\n noiseMultiplier: sgdNoiseMultiplier, numTrainingSteps, alphas});\n return convertRenyiToDP({alphas, rdps, targetDelta});\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":694,"value":"SGDepsilonValues = datasetParameters.map(computeSGDepsilon);","pinned":false,"hidden":false,"mode":"ojs"},{"id":154,"value":"md`## Labels and Constants`","pinned":false,"hidden":false,"mode":"ojs"},{"id":140,"value":"sweepOver = {\n switch(sweepOverName) {\n case numSamplesLabel:\n return 'numSamples';\n case batchSizeLabel:\n return 'batchSize';\n case ftrlNoiseMultiplierLabel:\n return 'ftrlNoiseMultiplier';\n case sgdNoiseMultiplierLabel:\n return 'sgdNoiseMultiplier';\n case numTrainingStepsLabel:\n return 'numTrainingSteps';\n case targetDeltaLabel:\n return 'targetDelta';\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":53,"value":"numSamplesLabel = \"Number of Samples\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"batchSizeLabel = \"Batch Size\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":48,"value":"ftrlNoiseMultiplierLabel = \"DP-FTRL Noise Multiplier\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1010,"value":"sgdNoiseMultiplierLabel = \"DP-SGD Noise Multiplier\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":190,"value":"numTrainingStepsLabel = \"Number of Training Steps\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":227,"value":"targetDeltaLabel = \"Target Delta\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"datasetParameterNames = [numSamplesLabel, batchSizeLabel,\n ftrlNoiseMultiplierLabel, sgdNoiseMultiplierLabel,\n numTrainingStepsLabel, targetDeltaLabel]","pinned":false,"hidden":false,"mode":"ojs"},{"id":110,"value":"datasetParametersBase = ({\n ftrlNoiseMultiplier: ftrlNoiseMultiplier,\n sgdNoiseMultiplier: sgdNoiseMultiplier,\n numSamples: numSamples,\n batchSize: batchSize,\n numTrainingSteps: numTrainingSteps,\n targetDelta: targetDelta,\n resetTree: resetTree,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":85,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs"},{"id":87,"value":"math = require('mathjs@7.6.0/dist/math.min.js')","pinned":false,"hidden":false,"mode":"ojs"},{"id":830,"value":"stdlib = require('https://unpkg.com/@stdlib/stdlib@0.0.70/dist/stdlib-math-base-special-flat.min.js')","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W37","stdlib":"1","titling":"auto"}