A tighter bound for graphical models.

We present a method to bound the partition function of a Boltzmann machine neural network with any odd-order polynomial. This is a direct extension of the mean-field bound, which is first order. We show that the third-order bound is strictly better than mean field. Additionally, we derive a third-order bound for the likelihood of sigmoid belief networks. Numerical experiments indicate that an error reduction of a factor of two is easily reached in the region where expansion-based approximations are useful.

Learning in higher order Boltzmann machines using linear response.

We introduce an efficient method for learning and inference in higher order Boltzmann machines. The method is based on mean field theory with the linear response correction. We compute the correlations using the exact and the approximated method for a fully connected third order network of ten neurons. In addition, we compare the results of the exact and approximate learning algorithm. Finally we use the presented method to solve the shifter problem. We conclude that the linear response approximation gives good results as long as the couplings are not too large.

Value of estrogenic recruitment before chemotherapy: first randomized trial in primary breast cancer.

PURPOSE: Several preclinical studies showed that short-term pretreatment of breast cancer cells with estrogens can increase the antitumor efficacy of different cytotoxic drugs. Some early clinical studies in patients with advanced breast cancer did seem to support these findings. Therefore, the efficacy of estrogenic recruitment followed by chemotherapy was compared with that of chemotherapy alone in a randomized phase III study in women with lymph node-positive primary breast cancer. PATIENTS AND METHODS: Three hundred twenty-eight patients with stage II/IIIA breast cancer who were younger than 66 years of age were randomly allocated to chemotherapy with fluorouracil, doxorubicin, and cyclophosphamide (FAC) or FAC plus pretreatment with ethinyl estradiol (EE(2)). FAC (500, 50, and 500 mg/m(2), respectively) was administered intravenously once every 4 weeks for four cycles. EE(2) (0.5 mg) was administered orally, both 24 hours and immediately preceding FAC chemotherapy. RESULTS: Patient and tumor characteristics and chemotherapy dosages were comparable in both treatment groups. Of 318 assessable patients, with a median follow-up of 6.8 years, 177 patients had a relapse and 127 died. No significant differences were observed between the two treatment groups with respect to relapse-free, local recurrence-free, and overall survival according to univariate and multivariate analyses adjusted for age, menopausal status, tumor size, grade, number of positive nodes, and steroid-receptor status. The power for the detection of an increase of 50% in the median relapse-free survival was 80%. CONCLUSION: Estrogenic recruitment of breast cancer cells before FAC chemotherapy did not influence the efficacy of adjuvant chemotherapy in stage II/IIIA breast cancer patients after a follow-up of 6.8 years.