Multi-iteration Stochastic Estimator
------------------------------------
The `Multi-Iteration stochastiC Estimator`_ (MICE) is an estimator of gradients to be used in stochastic optimization. It uses control variates to build a hierarchy of iterations, adaptively sampling to keep the statistical variance below tolerance in an optimal fashion, cost-wise. The tolerance on the statistical error decreases proportionally to the square of the gradient norm, thus, SGD-MICE converges linearly in strongly convex L-smooth functions.
.. _Multi-Iteration stochastiC Estimator: https://arxiv.org/abs/2011.01718
This python implementation of MICE is able to
* estimate expectations or finite sums of gradients of functions;
* choose the optimal sample sizes in order to minimize the sampling cost;
* build a hierarchy of iterations that minimizes the total work;
* use a resampling technique to compute the gradient norm, thus enforcing stability;
* define a tolerance on the norm of the gradient estimate or a maximum number of evaluations as a stopping criterion.
Using MICE
----------
Using MICE is as simple as
>>> import numpy as np
>>> from mice import MICE
>>>
>>>
>>> def gradient(x, thts):
>>> return x - thts
>>>
>>>
>>> def sampler(n):
>>> return np.random.random((n, 1))
>>>
>>>
>>> df = MICE(gradient , sampler=sampler)
>>> x = 10
>>> for i in range(10):
... grad = df(x)
... x = x - grad
However, it is flexible enough to tackle more complex problems.
For more information on how to use MICE and examples, check the `documentation`_.
.. _documentation: https://mice.readthedocs.io
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"description": "Multi-iteration Stochastic Estimator\n------------------------------------\n\nThe `Multi-Iteration stochastiC Estimator`_ (MICE) is an estimator of gradients to be used in stochastic optimization. It uses control variates to build a hierarchy of iterations, adaptively sampling to keep the statistical variance below tolerance in an optimal fashion, cost-wise. The tolerance on the statistical error decreases proportionally to the square of the gradient norm, thus, SGD-MICE converges linearly in strongly convex L-smooth functions.\n\n.. _Multi-Iteration stochastiC Estimator: https://arxiv.org/abs/2011.01718\n\nThis python implementation of MICE is able to\n\n* estimate expectations or finite sums of gradients of functions;\n\n* choose the optimal sample sizes in order to minimize the sampling cost;\n\n* build a hierarchy of iterations that minimizes the total work;\n\n* use a resampling technique to compute the gradient norm, thus enforcing stability;\n\n* define a tolerance on the norm of the gradient estimate or a maximum number of evaluations as a stopping criterion.\n\nUsing MICE\n----------\n\nUsing MICE is as simple as\n\n >>> import numpy as np\n >>> from mice import MICE\n >>>\n >>>\n >>> def gradient(x, thts):\n >>> return x - thts\n >>>\n >>>\n >>> def sampler(n):\n >>> return np.random.random((n, 1))\n >>>\n >>>\n >>> df = MICE(gradient , sampler=sampler)\n >>> x = 10\n >>> for i in range(10):\n ... grad = df(x)\n ... x = x - grad\n\n\nHowever, it is flexible enough to tackle more complex problems.\nFor more information on how to use MICE and examples, check the `documentation`_.\n\n.. _documentation: https://mice.readthedocs.io\n",
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