Optimization of the best element of the set of expressions - what kind of the optimization problem this is?
$begingroup$
Let the following expression describes the conditional probability of the translation of the source sequence to the target sequence (e.g. for the sentence-to-sentence translation in the neural machine translation, where xi and yj are the words in the source and target language respectively):
![P(y_{1}^{N_{T}}, theta) = prod_{i=1}^{N_{T}} P(y_{i}|y_{
This probability depends on the parameters theta of the translator function (e.g. the weights and biases of the neural network) and this probability is used as the objective function to be maximized, to find optimal parameters theta* and optimal choices yj that gives the maximum of this probability. This can be solved using gradient methods, backpropagation. That is fine.
But I am trying to consider the case when the neural machine translator generates multiple target sentences for the one source sentence. Some sentences can be complete junk, some sentences can be the parapharses of the target sentence and one sentence can be the optimal choice. So - I would like to optimize the parameters theta in such manner that the following function achieves maximum:
![max_{theta} big{P(u_{1}^{N_{T}}, theta), P(s_{1}^{N_{T}}, theta), P(t_{1}^{N_{T}}, theta), ... big}]
So - optimizer has multiple sub-objectives and the optimizer shold find one sub-objective who can achieve the maximum over all the other sub-objective and over all the theta parameters and choices of target translations u, s, t.
What kind of optimization problem this is? How to apply gradient methods to such max-function? Where to start?
optimization nonlinear-optimization neural-networks programming
asked Dec 26 '18 at 13:59
TomRTomR
263312
$endgroup$
add a comment |
$begingroup$
Let the following expression describes the conditional probability of the translation of the source sequence to the target sequence (e.g. for the sentence-to-sentence translation in the neural machine translation, where xi and yj are the words in the source and target language respectively):
![P(y_{1}^{N_{T}}, theta) = prod_{i=1}^{N_{T}} P(y_{i}|y_{
This probability depends on the parameters theta of the translator function (e.g. the weights and biases of the neural network) and this probability is used as the objective function to be maximized, to find optimal parameters theta* and optimal choices yj that gives the maximum of this probability. This can be solved using gradient methods, backpropagation. That is fine.
But I am trying to consider the case when the neural machine translator generates multiple target sentences for the one source sentence. Some sentences can be complete junk, some sentences can be the parapharses of the target sentence and one sentence can be the optimal choice. So - I would like to optimize the parameters theta in such manner that the following function achieves maximum:
![max_{theta} big{P(u_{1}^{N_{T}}, theta), P(s_{1}^{N_{T}}, theta), P(t_{1}^{N_{T}}, theta), ... big}]
So - optimizer has multiple sub-objectives and the optimizer shold find one sub-objective who can achieve the maximum over all the other sub-objective and over all the theta parameters and choices of target translations u, s, t.
What kind of optimization problem this is? How to apply gradient methods to such max-function? Where to start?
optimization nonlinear-optimization neural-networks programming
asked Dec 26 '18 at 13:59
TomRTomR
263312
$endgroup$
add a comment |
$begingroup$
Let the following expression describes the conditional probability of the translation of the source sequence to the target sequence (e.g. for the sentence-to-sentence translation in the neural machine translation, where xi and yj are the words in the source and target language respectively):
![P(y_{1}^{N_{T}}, theta) = prod_{i=1}^{N_{T}} P(y_{i}|y_{
This probability depends on the parameters theta of the translator function (e.g. the weights and biases of the neural network) and this probability is used as the objective function to be maximized, to find optimal parameters theta* and optimal choices yj that gives the maximum of this probability. This can be solved using gradient methods, backpropagation. That is fine.
But I am trying to consider the case when the neural machine translator generates multiple target sentences for the one source sentence. Some sentences can be complete junk, some sentences can be the parapharses of the target sentence and one sentence can be the optimal choice. So - I would like to optimize the parameters theta in such manner that the following function achieves maximum:
![max_{theta} big{P(u_{1}^{N_{T}}, theta), P(s_{1}^{N_{T}}, theta), P(t_{1}^{N_{T}}, theta), ... big}]
So - optimizer has multiple sub-objectives and the optimizer shold find one sub-objective who can achieve the maximum over all the other sub-objective and over all the theta parameters and choices of target translations u, s, t.
What kind of optimization problem this is? How to apply gradient methods to such max-function? Where to start?
optimization nonlinear-optimization neural-networks programming
asked Dec 26 '18 at 13:59
TomRTomR
263312
$endgroup$
Let the following expression describes the conditional probability of the translation of the source sequence to the target sequence (e.g. for the sentence-to-sentence translation in the neural machine translation, where xi and yj are the words in the source and target language respectively):
![P(y_{1}^{N_{T}}, theta) = prod_{i=1}^{N_{T}} P(y_{i}|y_{
This probability depends on the parameters theta of the translator function (e.g. the weights and biases of the neural network) and this probability is used as the objective function to be maximized, to find optimal parameters theta* and optimal choices yj that gives the maximum of this probability. This can be solved using gradient methods, backpropagation. That is fine.
But I am trying to consider the case when the neural machine translator generates multiple target sentences for the one source sentence. Some sentences can be complete junk, some sentences can be the parapharses of the target sentence and one sentence can be the optimal choice. So - I would like to optimize the parameters theta in such manner that the following function achieves maximum:
![max_{theta} big{P(u_{1}^{N_{T}}, theta), P(s_{1}^{N_{T}}, theta), P(t_{1}^{N_{T}}, theta), ... big}]
So - optimizer has multiple sub-objectives and the optimizer shold find one sub-objective who can achieve the maximum over all the other sub-objective and over all the theta parameters and choices of target translations u, s, t.
What kind of optimization problem this is? How to apply gradient methods to such max-function? Where to start?
optimization nonlinear-optimization neural-networks programming
optimization nonlinear-optimization neural-networks programming
asked Dec 26 '18 at 13:59
TomRTomR
263312
asked Dec 26 '18 at 13:59
TomRTomR
263312
edited Dec 26 '18 at 14:14
TomR
asked Dec 26 '18 at 13:59
TomRTomR
263312
asked Dec 26 '18 at 13:59
TomRTomR
263312
asked Dec 26 '18 at 13:59
TomRTomR
263312
263312
add a comment |
add a comment |
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