Federated Linear Regression

Linear Regression(LinR) is a simple statistic model widely used for predicting continuous numbers. FATE provides Heterogeneous Linear Regression(HeteroLinR). HeteroLinR also supports multi-Host training. You can specify multiple hosts in the job configuration file like the provided examples/dsl/v2/hetero_linear_regression.

Here we simplify participants of the federation process into three parties. Party A represents Guest, party B represents Host. Party C, which is also known as “Arbiter,” is a third party that works as coordinator. Party C is responsible for generating private and public keys.

Heterogeneous LinR

The process of HeteroLinR training is shown below:

A sample alignment process is conducted before training. The sample alignment process identifies overlapping samples in databases of all parties. The federated model is built based on the overlapping samples. The whole sample alignment process is conducted in encryption mode, and so confidential information (e.g. sample ids) will not be leaked.

In the training process, party A and party B each compute the elements needed for final gradients. Arbiter aggregates, calculates, and transfers back the final gradients to corresponding parties. For more details on the secure model-building process, please refer to this paper.

Param

linear_regression_param

Classes

LinearParam (LinearModelParam)

Parameters used for Linear Regression.

Parameters:

Name	Type	Description	Default
penalty	{'L2' or 'L1'}	Penalty method used in LinR. Please note that, when using encrypted version in HeteroLinR, 'L1' is not supported.	'L2'
tol	float, default: 1e-4	The tolerance of convergence	0.0001
alpha	float, default: 1.0	Regularization strength coefficient.	1.0
optimizer	{'sgd', 'rmsprop', 'adam', 'sqn', 'adagrad'}	Optimize method	'sgd'
batch_size	int, default: -1	Batch size when updating model. -1 means use all data in a batch. i.e. Not to use mini-batch strategy.	-1
learning_rate	float, default: 0.01	Learning rate	0.01
max_iter	int, default: 20	The maximum iteration for training.	20
init_param	InitParam object, default: default InitParam object	Init param method object.	<federatedml.param.init_model_param.InitParam object at 0x7fbb715fd590>
early_stop	{'diff', 'abs', 'weight_dff'}	Method used to judge convergence. a) diff： Use difference of loss between two iterations to judge whether converge. b) abs: Use the absolute value of loss to judge whether converge. i.e. if loss < tol, it is converged. c) weight_diff: Use difference between weights of two consecutive iterations	'diff'
encrypt_param	EncryptParam object, default: default EncryptParam object	encrypt param	<federatedml.param.encrypt_param.EncryptParam object at 0x7fbb71666950>
encrypted_mode_calculator_param	EncryptedModeCalculatorParam object, default: default EncryptedModeCalculatorParam object	encrypted mode calculator param	<federatedml.param.encrypted_mode_calculation_param.EncryptedModeCalculatorParam object at 0x7fbb71666ad0>
cv_param	CrossValidationParam object, default: default CrossValidationParam object	cv param	<federatedml.param.cross_validation_param.CrossValidationParam object at 0x7fbb71666a50>
decay	int or float, default: 1	Decay rate for learning rate. learning rate will follow the following decay schedule. lr = lr0/(1+decay*t) if decay_sqrt is False. If decay_sqrt is True, lr = lr0 / sqrt(1+decay*t) where t is the iter number.	1
decay_sqrt	Bool, default: True	lr = lr0/(1+decay*t) if decay_sqrt is False, otherwise, lr = lr0 / sqrt(1+decay*t)	True
validation_freqs	int, list, tuple, set, or None	validation frequency during training, required when using early stopping. The default value is None, 1 is suggested. You can set it to a number larger than 1 in order to speed up training by skipping validation rounds. When it is larger than 1, a number which is divisible by "max_iter" is recommended, otherwise, you will miss the validation scores of the last training iteration.	None
early_stopping_rounds	int, default: None	If positive number specified, at every specified training rounds, program checks for early stopping criteria. Validation_freqs must also be set when using early stopping.	None
metrics	list or None, default: None	Specify which metrics to be used when performing evaluation during training process. If metrics have not improved at early_stopping rounds, trianing stops before convergence. If set as empty, default metrics will be used. For regression tasks, default metrics are ['root_mean_squared_error', 'mean_absolute_error']	None
use_first_metric_only	bool, default: False	Indicate whether to use the first metric in metrics as the only criterion for early stopping judgement.	False
floating_point_precision	None or integer	if not None, use floating_point_precision-bit to speed up calculation, e.g.: convert an x to round(x * 2**floating_point_precision) during Paillier operation, divide the result by 2**floating_point_precision in the end.	23
callback_param	CallbackParam object	callback param	<federatedml.param.callback_param.CallbackParam object at 0x7fbb71666b10>

Source code in federatedml/param/linear_regression_param.py

class LinearParam(LinearModelParam):
    """
    Parameters used for Linear Regression.

    Parameters
    ----------
    penalty : {'L2' or 'L1'}
        Penalty method used in LinR. Please note that, when using encrypted version in HeteroLinR,
        'L1' is not supported.

    tol : float, default: 1e-4
        The tolerance of convergence

    alpha : float, default: 1.0
        Regularization strength coefficient.

    optimizer : {'sgd', 'rmsprop', 'adam', 'sqn', 'adagrad'}
        Optimize method

    batch_size : int, default: -1
        Batch size when updating model. -1 means use all data in a batch. i.e. Not to use mini-batch strategy.

    learning_rate : float, default: 0.01
        Learning rate

    max_iter : int, default: 20
        The maximum iteration for training.

    init_param: InitParam object, default: default InitParam object
        Init param method object.

    early_stop : {'diff', 'abs', 'weight_dff'}
        Method used to judge convergence.
            a)	diff： Use difference of loss between two iterations to judge whether converge.
            b)	abs: Use the absolute value of loss to judge whether converge. i.e. if loss < tol, it is converged.
            c)  weight_diff: Use difference between weights of two consecutive iterations

    encrypt_param: EncryptParam object, default: default EncryptParam object
        encrypt param

    encrypted_mode_calculator_param: EncryptedModeCalculatorParam object, default: default EncryptedModeCalculatorParam object
        encrypted mode calculator param

    cv_param: CrossValidationParam object, default: default CrossValidationParam object
        cv param

    decay: int or float, default: 1
        Decay rate for learning rate. learning rate will follow the following decay schedule.
        lr = lr0/(1+decay*t) if decay_sqrt is False. If decay_sqrt is True, lr = lr0 / sqrt(1+decay*t)
        where t is the iter number.

    decay_sqrt: Bool, default: True
        lr = lr0/(1+decay*t) if decay_sqrt is False, otherwise, lr = lr0 / sqrt(1+decay*t)

    validation_freqs: int, list, tuple, set, or None
        validation frequency during training, required when using early stopping.
        The default value is None, 1 is suggested. You can set it to a number larger than 1 in order to speed up training by skipping validation rounds.
        When it is larger than 1, a number which is divisible by "max_iter" is recommended, otherwise, you will miss the validation scores of the last training iteration.

    early_stopping_rounds: int, default: None
        If positive number specified, at every specified training rounds, program checks for early stopping criteria.
        Validation_freqs must also be set when using early stopping.

    metrics: list or None, default: None
        Specify which metrics to be used when performing evaluation during training process. If metrics have not improved at early_stopping rounds, trianing stops before convergence.
        If set as empty, default metrics will be used. For regression tasks, default metrics are ['root_mean_squared_error', 'mean_absolute_error']

    use_first_metric_only: bool, default: False
        Indicate whether to use the first metric in `metrics` as the only criterion for early stopping judgement.

    floating_point_precision: None or integer
        if not None, use floating_point_precision-bit to speed up calculation,
        e.g.: convert an x to round(x * 2**floating_point_precision) during Paillier operation, divide
                the result by 2**floating_point_precision in the end.
    callback_param: CallbackParam object
        callback param

    """

    def __init__(self, penalty='L2',
                 tol=1e-4, alpha=1.0, optimizer='sgd',
                 batch_size=-1, learning_rate=0.01, init_param=InitParam(),
                 max_iter=20, early_stop='diff',
                 encrypt_param=EncryptParam(), sqn_param=StochasticQuasiNewtonParam(),
                 encrypted_mode_calculator_param=EncryptedModeCalculatorParam(),
                 cv_param=CrossValidationParam(), decay=1, decay_sqrt=True, validation_freqs=None,
                 early_stopping_rounds=None, stepwise_param=StepwiseParam(), metrics=None, use_first_metric_only=False,
                 floating_point_precision=23, callback_param=CallbackParam()):
        super(LinearParam, self).__init__(penalty=penalty, tol=tol, alpha=alpha, optimizer=optimizer,
                                          batch_size=batch_size, learning_rate=learning_rate,
                                          init_param=init_param, max_iter=max_iter, early_stop=early_stop,
                                          encrypt_param=encrypt_param, cv_param=cv_param, decay=decay,
                                          decay_sqrt=decay_sqrt, validation_freqs=validation_freqs,
                                          early_stopping_rounds=early_stopping_rounds,
                                          stepwise_param=stepwise_param, metrics=metrics,
                                          use_first_metric_only=use_first_metric_only,
                                          floating_point_precision=floating_point_precision,
                                          callback_param=callback_param)
        self.sqn_param = copy.deepcopy(sqn_param)
        self.encrypted_mode_calculator_param = copy.deepcopy(encrypted_mode_calculator_param)

    def check(self):
        descr = "linear_regression_param's "
        super(LinearParam, self).check()
        if self.optimizer not in ['sgd', 'rmsprop', 'adam', 'adagrad', 'sqn']:
            raise ValueError(
                descr + "optimizer not supported, optimizer should be"
                        " 'sgd', 'rmsprop', 'adam', 'sqn' or 'adagrad'")
        self.sqn_param.check()
        if self.encrypt_param.method != consts.PAILLIER:
            raise ValueError(
                descr + "encrypt method supports 'Paillier' only")
        return True

__init__(self, penalty='L2', tol=0.0001, alpha=1.0, optimizer='sgd', batch_size=-1, learning_rate=0.01, init_param=<federatedml.param.init_model_param.InitParam object at 0x7fbb715fd590>, max_iter=20, early_stop='diff', encrypt_param=<federatedml.param.encrypt_param.EncryptParam object at 0x7fbb71666950>, sqn_param=<federatedml.param.sqn_param.StochasticQuasiNewtonParam object at 0x7fbb71666810>, encrypted_mode_calculator_param=<federatedml.param.encrypted_mode_calculation_param.EncryptedModeCalculatorParam object at 0x7fbb71666ad0>, cv_param=<federatedml.param.cross_validation_param.CrossValidationParam object at 0x7fbb71666a50>, decay=1, decay_sqrt=True, validation_freqs=None, early_stopping_rounds=None, stepwise_param=<federatedml.param.stepwise_param.StepwiseParam object at 0x7fbb71666b50>, metrics=None, use_first_metric_only=False, floating_point_precision=23, callback_param=<federatedml.param.callback_param.CallbackParam object at 0x7fbb71666b10>) special

Source code in federatedml/param/linear_regression_param.py

def __init__(self, penalty='L2',
             tol=1e-4, alpha=1.0, optimizer='sgd',
             batch_size=-1, learning_rate=0.01, init_param=InitParam(),
             max_iter=20, early_stop='diff',
             encrypt_param=EncryptParam(), sqn_param=StochasticQuasiNewtonParam(),
             encrypted_mode_calculator_param=EncryptedModeCalculatorParam(),
             cv_param=CrossValidationParam(), decay=1, decay_sqrt=True, validation_freqs=None,
             early_stopping_rounds=None, stepwise_param=StepwiseParam(), metrics=None, use_first_metric_only=False,
             floating_point_precision=23, callback_param=CallbackParam()):
    super(LinearParam, self).__init__(penalty=penalty, tol=tol, alpha=alpha, optimizer=optimizer,
                                      batch_size=batch_size, learning_rate=learning_rate,
                                      init_param=init_param, max_iter=max_iter, early_stop=early_stop,
                                      encrypt_param=encrypt_param, cv_param=cv_param, decay=decay,
                                      decay_sqrt=decay_sqrt, validation_freqs=validation_freqs,
                                      early_stopping_rounds=early_stopping_rounds,
                                      stepwise_param=stepwise_param, metrics=metrics,
                                      use_first_metric_only=use_first_metric_only,
                                      floating_point_precision=floating_point_precision,
                                      callback_param=callback_param)
    self.sqn_param = copy.deepcopy(sqn_param)
    self.encrypted_mode_calculator_param = copy.deepcopy(encrypted_mode_calculator_param)

check(self)

Source code in federatedml/param/linear_regression_param.py

def check(self):
    descr = "linear_regression_param's "
    super(LinearParam, self).check()
    if self.optimizer not in ['sgd', 'rmsprop', 'adam', 'adagrad', 'sqn']:
        raise ValueError(
            descr + "optimizer not supported, optimizer should be"
                    " 'sgd', 'rmsprop', 'adam', 'sqn' or 'adagrad'")
    self.sqn_param.check()
    if self.encrypt_param.method != consts.PAILLIER:
        raise ValueError(
            descr + "encrypt method supports 'Paillier' only")
    return True

Features

1. L1 & L2 regularization

2. Mini-batch mechanism

3. Five optimization methods:

   • sgd
     gradient descent with arbitrary batch size

   • rmsprop
     RMSProp

   • adam
     Adam

   • adagrad
     AdaGrad

   • nesterov_momentum_sgd
     Nesterov Momentum

   • stochastic quansi-newton
     The algorithm details can refer to this paper.

4. Three converge criteria:

   • diff
     Use difference of loss between two iterations, not available for multi-host training

   • abs
     Use the absolute value of loss

   • weight_diff
     Use difference of model weights

5. Support multi-host modeling task. For details on how to configure for multi-host modeling task, please refer to this guide

6. Support validation for every arbitrary iterations

7. Learning rate decay mechanism

8. Support early stopping mechanism, which checks for performance change on specified metrics over training rounds. Early stopping is triggered when no improvement is found at early stopping rounds.

9. Support sparse format data as input.

10. Support stepwise. For details on stepwise mode, please refer to stepwise .

Hetero-SSHE-LinR features:

1. L1 & L2 regularization

2. Mini-batch mechanism

3. Support different encrypt-mode to balance speed and security

4. Support early-stopping mechanism

5. Support setting arbitrary metrics for validation during training

6. Support model encryption with host model

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Last update: 2022-03-30