An estimation method utilizing a pair of target-directional models 106 and 108 includes the steps 160 and 164 of decoding an input 142 utilizing the first and the second models 106 and 108, thereby producing k-best hypotheses 162 and 166 from each of the first and the second models 106 and 108; calculating a union of the k-best hypotheses, and re-scoring 168 each of the best hypotheses in the union utilizing the first and the second models; and selecting a hypothesis 144 with the highest score.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method of training a first sequence-to-sequence estimation model and a second sequence-to-sequence estimation model, said method comprising: a step of preparing pairs of sequences in first storage, each pair including a source sequence and a target sequence; a first step of concatenating a source sequence and a target sequence of each of the pairs of sequences stored in the first storage, thereby generating a first set of concatenated sequences and storing the first set in second storage; a first step of training the first sequence-to-sequence estimation model utilizing the first set of concatenated sequences stored in the second storage. a step of permuting a target sequence of each of the pairs of sequences by a first permuting function executed by the computer, thereby producing a permuted target sequence for each of the pairs of sequences; a second step of concatenating a source sequence of each of the pairs of sequences and the permuted target sequence paired with the source sequence, thereby generating a second set of concatenated sequences and storing the second set in third storage; a second step of training the second sequence-to-sequence estimation model utilizing the second set of concatenated sequences stored in the third storage. 2. The method in accordance with claim 1, wherein the permuting function is a function reversing the order of tokens in an input sequence. 3. The method in accordance with claim 2 wherein each of the first and the second sequence-to-sequence estimation models are RNNs. 4. A computer-implemented joint estimation method utilizing the first and the second sequence-to-sequence estimation models trained by the method in accordance with claim 1, comprising the steps of: receiving an input sequence as an input of the computer; decoding the input utilizing the first and the second sequence-to-sequence estimation models, thereby producing a prescribed number of best hypotheses from each of the first and the second sequence-to-sequence models; permuting tokens by a second permuting function executed by the computer, in each of the prescribed number of best hypotheses output from the second sequence-to-sequence estimation model; re-scoring each of the best hypotheses output from the first sequence-to-sequence estimation model and the best hypothesis with tokens permuted in the permuting step utilizing the first and the second sequence-to-sequence estimation models; and selecting a hypothesis with the highest score in the re-scoring step as an estimated output corresponding to the input. 5. The joint estimation method in accordance with claim 4, wherein, the second permuting function being an inverse of the first permuting function. 6. The joint estimation method in accordance with claim 5, wherein the permuting function is a function reversing the order of tokens in an input sequence. 7. The joint estimation method in accordance with claim 6, wherein each of the first and the second sequence-to-sequence estimation models are RNNs. 8. The joint estimation method in accordance with claim 4 wherein the re-scoring step includes the steps of: calculating a union set of the best hypotheses output from the first sequence-to-sequence estimation model and the best hypotheses output from the second sequence-to-sequence estimation model with tokens permuted in the permuting step; computing a first score of each of the hypotheses in the union set utilizing the first sequence-to-sequence estimation model; computing a second score of each of the hypotheses in the union set utilizing the second sequence-to-sequence estimation model; and re-scoring each of the hypotheses in the union set by multiplying the first score by the second score. 9. The joint estimation method in accordance with claim 4 wherein the re-scoring step includes the steps of: calculating a union set of the best hypotheses output from the first sequence-to-sequence estimation model and the best hypotheses output from the second sequence-to-sequence estimation model with tokens permuted in the permuting step; generating a set of new hypotheses by concatenating any one of prefixes in the hypotheses in the union set and any one of suffixes in the hypotheses in the union set; computing a first score of each of the new hypotheses utilizing the first sequence-to-sequence estimation model; computing a second score of each of the new hypotheses utilizing the second sequence-to-sequence estimation model; and re-scoring each of the new hypotheses by multiplying the first score by the second score. 10. A computer-implemented joint estimation apparatus utilizing the first and the second sequence-to-sequence estimation models trained by the method in accordance with claim 1, the apparatus comprising: a data receiving interface connected to the computer, configured to receive an input sequence as an input; a storage device connected to the computer, for storing the first and the second sequence-to-sequence estimation models; and a control unit configured to; decode the input utilizing the first and the second sequence-to-sequence estimation models, thereby producing a prescribed number of best hypotheses from each of the first and the second sequence-to-sequence models; permute tokens by executing a second permuting function, in each of the prescribed number of best hypotheses output from the second sequence-to-sequence estimation model; re-score each of the best hypotheses output from the first sequence-to-sequence estimation model and the best hypothesis with tokens permuted in the permuting step utilizing the first and the second sequence-to-sequence estimation models; and select a hypothesis with the highest score in the re-scoring step as an estimated output corresponding to the input. 11. The joint estimation apparatus in accordance with claim 10, wherein, the second permuting function being an inverse of the first permuting function. 12. The joint estimation method in accordance with claim 11, wherein the permuting function is a function reversing the order of tokens in an input sequence. 13. The joint estimation apparatus in accordance with claim 12, wherein each of the first and the second sequence-to-sequence estimation models are RNNs. 14. The joint estimation apparatus in accordance with claim 10 wherein in re-scoring, the control unit is configured to calculate a union set of the best hypotheses output from the first sequence-to-sequence estimation model and the best hypotheses output from the second sequence-to-sequence estimation model with tokens permuted; compute a first score of each of the hypotheses in the union set utilizing the first sequence-to-sequence estimation model; compute a second score of each of the hypotheses in the union set utilizing the second sequence-to-sequence estimation model; and re-score each of the hypotheses in the union set by multiplying the first score by the second score. 15. The joint estimation apparatus in accordance with claim 10 wherein in rescoring, the control unit is configured to calculate a union set of the best hypotheses output from the first sequence-to-sequence estimation model and the best hypotheses output from the second sequence-to-sequence estimation model with tokens permuted; generate a set of new hypotheses by concatenating any one of prefixes in the hypotheses in the union set and any on of suffixes in the hypotheses in the union set; compute a first score of each of the new hypotheses utilizing the first sequence-to-sequence estimation model; compute a second score of each of the new hypotheses utilizing the second sequence-to-sequence estimation model; and re-score each of the new hypotheses by multiplying the first score by the second score.