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"source": [
"# T4 - Optimization of Infection Duration"
]
},
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"cell_type": "markdown",
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"source": [
"In this tutorial, we'll introduce the concept of parameter optimization against an optimization function -- in this case, maximizing the mean infection duration in naive infectious challenges by changing the antigenic switching rate parameter."
]
},
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"attachments": {},
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"source": [
"We'll start by defining a function to perform multi-individual challenges (similar to the last tutorial)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": "import numpy as np\nimport pandas as pd\nimport xarray as xr\nimport matplotlib.pyplot as plt\n\nfrom emodlib.malaria import IntrahostComponent, create_config\n\n\ndef multiple_challenges(config, n_people, duration):\n \n asexuals = np.zeros((n_people, duration))\n gametocytes = np.zeros((n_people, duration))\n pp = [IntrahostComponent.create(config) for _ in range(n_people)]\n _ = [p.challenge() for p in pp]\n\n for t in range(duration):\n for i, p in enumerate(pp):\n p.update(dt=1)\n asexuals[i, t] = p.parasite_density\n gametocytes[i, t] = p.gametocyte_density\n \n da = xr.DataArray(dims=('individual', 'time', 'channel'),\n coords=(range(n_people), range(duration), ['parasite_density', 'gametocyte_density']))\n \n da.loc[dict(channel='parasite_density')] = asexuals\n da.loc[dict(channel='gametocyte_density')] = gametocytes\n \n return da"
},
{
"attachments": {},
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"source": [
"We'll also define a helper function to determine the duration of challenge infections based on the time index of the last non-zero parasite density"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def get_last_nonzero_by_row(A):\n",
" \"\"\" https://stackoverflow.com/a/39959511 \"\"\"\n",
" return np.arange(A.shape[0]), A.shape[1] - 1 - (A[:, ::-1]!=0).argmax(1)"
]
},
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"source": "Then we'll define our objective function:\n- log-uniform sampling of the antigen switching rate within a defined range\n- creating a model config with that parameter value\n- running the multi-individual challenge time-series\n- returning the mean infection-duration value"
},
{
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"execution_count": null,
"metadata": {},
"outputs": [],
"source": "def objective(trial):\n \n n_people = 50\n duration = 500\n\n antigen_switch_rate = trial.suggest_float(\"Antigen_Switch_Rate\", 5e-10, 5e-8, log=True)\n config = create_config({'infection_params': {'Antigen_Switch_Rate': antigen_switch_rate}})\n \n da = multiple_challenges(config, duration=duration, n_people=n_people)\n infection_durations = get_last_nonzero_by_row(da.sel(channel='parasite_density').values)[1]\n \n return infection_durations.mean()"
},
{
"attachments": {},
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"source": [
"Finally, we'll create an optuna study and run a number of optimization trials..."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
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"text": [
"\u001b[32m[I 2023-05-26 18:53:14,086]\u001b[0m A new study created in memory with name: maximize_duration\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,124]\u001b[0m Trial 0 finished with value: 249.32 and parameters: {'Antigen_Switch_Rate': 1.1915470318960563e-09}. Best is trial 0 with value: 249.32.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,171]\u001b[0m Trial 1 finished with value: 399.04 and parameters: {'Antigen_Switch_Rate': 2.750348541347495e-09}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,218]\u001b[0m Trial 2 finished with value: 321.86 and parameters: {'Antigen_Switch_Rate': 1.2742403528792963e-08}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,257]\u001b[0m Trial 3 finished with value: 291.14 and parameters: {'Antigen_Switch_Rate': 1.4323327599950657e-09}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,303]\u001b[0m Trial 4 finished with value: 351.2 and parameters: {'Antigen_Switch_Rate': 7.727469068951856e-09}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,351]\u001b[0m Trial 5 finished with value: 280.38 and parameters: {'Antigen_Switch_Rate': 4.6148422747495935e-08}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,383]\u001b[0m Trial 6 finished with value: 170.26 and parameters: {'Antigen_Switch_Rate': 5.363872536158119e-10}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,429]\u001b[0m Trial 7 finished with value: 359.2 and parameters: {'Antigen_Switch_Rate': 6.2266808194259075e-09}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,475]\u001b[0m Trial 8 finished with value: 342.46 and parameters: {'Antigen_Switch_Rate': 8.715215269434397e-09}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,508]\u001b[0m Trial 9 finished with value: 184.14 and parameters: {'Antigen_Switch_Rate': 6.224321379915857e-10}. Best is trial 1 with value: 399.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,557]\u001b[0m Trial 10 finished with value: 400.04 and parameters: {'Antigen_Switch_Rate': 2.7055736726897753e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,603]\u001b[0m Trial 11 finished with value: 386.52 and parameters: {'Antigen_Switch_Rate': 2.7040378193028815e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,650]\u001b[0m Trial 12 finished with value: 399.72 and parameters: {'Antigen_Switch_Rate': 3.0708647379292074e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,697]\u001b[0m Trial 13 finished with value: 393.78 and parameters: {'Antigen_Switch_Rate': 3.2067748660456205e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,744]\u001b[0m Trial 14 finished with value: 394.92 and parameters: {'Antigen_Switch_Rate': 4.169512643087303e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,786]\u001b[0m Trial 15 finished with value: 332.96 and parameters: {'Antigen_Switch_Rate': 1.6758842380026993e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,832]\u001b[0m Trial 16 finished with value: 385.66 and parameters: {'Antigen_Switch_Rate': 4.51732112640819e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,876]\u001b[0m Trial 17 finished with value: 363.84 and parameters: {'Antigen_Switch_Rate': 2.1226773056736917e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,913]\u001b[0m Trial 18 finished with value: 236.3 and parameters: {'Antigen_Switch_Rate': 9.94876719956596e-10}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:14,957]\u001b[0m Trial 19 finished with value: 370.66 and parameters: {'Antigen_Switch_Rate': 1.814725113148747e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:15,007]\u001b[0m Trial 20 finished with value: 396.76 and parameters: {'Antigen_Switch_Rate': 4.011620108155682e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:15,053]\u001b[0m Trial 21 finished with value: 391.16 and parameters: {'Antigen_Switch_Rate': 2.86932123142975e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:15,098]\u001b[0m Trial 22 finished with value: 375.62 and parameters: {'Antigen_Switch_Rate': 2.2297814196138632e-09}. Best is trial 10 with value: 400.04.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:15,145]\u001b[0m Trial 23 finished with value: 409.2 and parameters: {'Antigen_Switch_Rate': 2.9439327747062316e-09}. Best is trial 23 with value: 409.2.\u001b[0m\n",
"\u001b[32m[I 2023-05-26 18:53:15,182]\u001b[0m Trial 24 finished with value: 238.94 and parameters: {'Antigen_Switch_Rate': 9.439553321717197e-10}. Best is trial 23 with value: 409.2.\u001b[0m\n"
]
}
],
"source": [
"import optuna\n",
"\n",
"study = optuna.create_study(study_name='maximize_duration', direction='maximize')\n",
"study.optimize(objective, n_trials=25)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
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"data": {
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"{'Antigen_Switch_Rate': 2.9439327747062316e-09}"
]
},
"execution_count": 5,
"metadata": {},
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],
"source": [
"study.best_params # parameter for longest avg duration"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
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"data": {
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},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"study.best_value # longest avg duration"
]
},
{
"attachments": {},
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"source": [
"Now let's look at a few default visualizations of the optuna study:\n",
"- the convergence towards maximizing the objective value over successive trials\n",
"- the value of the objective as a function of our 1-d parameter range explored"
]
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