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Sparse estimation of a Gaussian graphical model (GGM) is an important technique for making relationships between observed variables more interpretable. Various methods have been proposed for sparse GGM estimation, including the graphical lasso that uses the ℓ 1 norm regularization term, and other methods that use nonconvex regularization terms. Most of these methods approximate the ℓ 0 (pseudo) norm by more tractable functions; however, to estimate more accurate solutions, it is preferable to directly use the ℓ 0 norm for counting the number of nonzero elements. To this end, we focus on sparse estimation of GGM with the cardinality constraint based on the ℓ 0 norm. Specifically, we convert the cardinality constraint into an equivalent constraint based on the largest- K norm, and reformulate the resultant constrained optimization problem into an unconstrained penalty form with a DC (difference of convex functions) representation. To solve this problem efficiently, we design a DC algorithm in which the graphical lasso algorithm is repeatedly executed to solve convex optimization subproblems. Experimental results using two synthetic datasets show that our method achieves results that are comparable to or better than conventional methods for sparse GGM estimation. Our method is particularly advantageous for selecting true edges when cross-validation is used to determine the number of edges. Moreover, our DC algorithm converges within a practical time frame compared to the graphical lasso.

This paper studies mean-risk portfolio optimization models using the conditional value-at-risk (CVaR) as a risk measure. We also employ a cardinality constraint for limiting the number of invested assets. Solving such a cardinality-constrained mean-CVaR model is computationally challenging for two main reasons. First, this model is formulated as a mixed-integer optimization (MIO) problem because of the cardinality constraint, so solving it exactly is very hard when the number of investable assets is large. Second, the problem size depends on the number of asset return scenarios, and the computational efficiency decreases when the number of scenarios is large. To overcome these challenges, we propose a high-performance algorithm named the bilevel cutting-plane algorithm for exactly solving the cardinality-constrained mean-CVaR portfolio optimization problem. We begin by reformulating the problem as a bilevel optimization problem and then develop a cutting-plane algorithm for solving the upper-level problem. To speed up computations for cut generation, we apply to the lower-level problem another cutting-plane algorithm for efficiently minimizing CVaR with a large number of scenarios. Moreover, we prove the convergence properties of our bilevel cutting-plane algorithm. Numerical experiments demonstrate that, compared with other MIO approaches, our algorithm can provide optimal solutions to large problem instances faster.

In order to provide high-quality recommendations for users, it is desirable to share and integrate multiple datasets held by different parties. However, when sharing such distributed datasets, we need to protect personal and confidential information contained in the datasets. To this end, we establish a framework for privacy-preserving recommender systems using the data collaboration analysis of distributed datasets. Numerical experiments with two public rating datasets demonstrate that our privacy-preserving method for rating prediction can improve the prediction accuracy for distributed datasets. More precisely, compared to the individual analysis in which each party analyzes only its own dataset, our method reduced prediction errors by an average of 4.5% and up to 7.0%. This study opens up new possibilities for privacy-preserving techniques in recommender systems.

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that the forecast for an upper-level time series equals the sum of forecasts for corresponding lower-level time series. Previous methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts and then reconciling those forecasts based on their inherent hierarchical structure. To improve time series predictions, we propose a structured regularization method for completing both phases simultaneously. The proposed method is based on a prediction model for bottom-level time series and uses a structured regularization term to incorporate upper-level forecasts into the prediction model. We also develop a backpropagation algorithm specialized for applying our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate that our method is comparable in terms of prediction accuracy and computational efficiency to other methods for time series prediction.

We present a mixed-integer optimization (MIO) approach to sparse Poisson regression. The MIO approach to sparse linear regression was first proposed in the 1970s, but has recently received renewed attention due to advances in optimization algorithms and computer hardware. In contrast to many sparse estimation algorithms, the MIO approach has the advantage of finding the best subset of explanatory variables with respect to various criterion functions. In this paper, we focus on a sparse Poisson regression that maximizes the weighted sum of the log-likelihood function and the L 2 -regularization term. For this problem, we derive a mixed-integer quadratic optimization (MIQO) formulation by applying a piecewise-linear approximation to the log-likelihood function. Optimization software can solve this MIQO problem to optimality. Moreover, we propose two methods for selecting a limited number of tangent lines effective for piecewise-linear approximations. We assess the efficacy of our method through computational experiments using synthetic and real-world datasets. Our methods provide better log-likelihood values than do conventional greedy algorithms in selecting tangent lines. In addition, our MIQO formulation delivers better out-of-sample prediction performance than do forward stepwise selection and L 1 -regularized estimation, especially in low-noise situations.

Multicollinearity exists when some explanatory variables of a multiple linear regression model are highly correlated. High correlation among explanatory variables reduces the reliability of the analysis. To eliminate multicollinearity from a linear regression model, we consider how to select a subset of significant variables by means of the variance inflation factor (VIF), which is the most common indicator used in detecting multicollinearity. In particular, we adopt the mixed integer optimization (MIO) approach to subset selection. The MIO approach was proposed in the 1970s, and recently it has received renewed attention due to advances in algorithms and hardware. However, none of the existing studies have developed a computationally tractable MIO formulation for eliminating multicollinearity on the basis of VIF. In this paper, we propose mixed integer quadratic optimization (MIQO) formulations for selecting the best subset of explanatory variables subject to the upper bounds on the VIFs of selected variables. Our two MIQO formulations are based on the two equivalent definitions of VIF. Computational results illustrate the effectiveness of our MIQO formulations by comparison with conventional local search algorithms and MIO-based cutting plane algorithms.

This paper concerns a method of selecting a subset of features for a logistic regression model. Information criteria, such as the Akaike information criterion and Bayesian information criterion, are employed as a goodness-of-fit measure. The purpose of our work is to establish a computational framework for selecting a subset of features with an optimality guarantee. For this purpose, we devise mixed integer optimization formulations for feature subset selection in logistic regression. Specifically, we pose the problem as a mixed integer linear optimization problem, which can be solved with standard mixed integer optimization software, by making a piecewise linear approximation of the logistic loss function. The computational results demonstrate that when the number of candidate features was less than 40, our method successfully provided a feature subset that was sufficiently close to an optimal one in a reasonable amount of time. Furthermore, even if there were more candidate features, our method often found a better subset of features than the stepwise methods did in terms of information criteria.

Percutaneous transhepatic gallbladder drainage (PTGBD) is an alternative to percutaneous transhepatic biliary drainage (PTBD) for cases with obstructive jaundice in which the bile duct obstruction is below the confluence of the cystic ducts. This retrospective study aimed to evaluate the usefulness of PTGBD and PTBD in patients with obstructive jaundice. We recruited patients who had undergone percutaneous biliary drainage for acute cholangitis and obstructive jaundice at two institutions between January 2017 and March 2024. In principle, PTBD was the first choice. PTGBD was selected for cases where the intrahepatic bile duct diameter was ≤ 5 mm or ≥ 6 mm with significant respiratory-related variability of the positioning of the bile ducts. In other cases, PTBD was chosen. Fifty-five patients were included in this analysis. However, patients with intrahepatic or hilar bile duct stenosis, post choledocholithiasis, complex cholecystitis, total bilirubin levels of < 2.0 mg/dL, and uncorrectable bleeding tendency and those who had undergone the procedure and later discontinued without puncture were excluded. The technical success rates, clinical success rates, and complication rates of the procedure were evaluated. The technical success rates were 96.3% (26/27) and 82.1% (23/28) in the PTGBD and PTBD groups, respectively. The clinical success rates were 85.2% (23/27) and 67.9% (19/28) in the PTGBD and PTBD groups, respectively. The complication rates were 18.5% (5/27) and 25.0% (7/28) in the PTGBD and PTBD groups, respectively. No serious complications were observed in either group. Hence, the two groups did not significantly differ in any of the endpoints. The outcomes of PTGBD were comparable to those of PTBD in patients with obstructive jaundice. Hence, PTGBD is a reasonable treatment option for cases of obstructive jaundice in which PTBD is not feasible.

Background and Objectives: Chondroitin sulfate ABC endolyase (condoliase) was launched as a new drug for chemonucleolysis in 2018. Few studies assessed its clinical outcomes, and many important factors remain unclear. This study aimed to clarify the preoperative conditions in which condoliase could be highly effective. Materials and Methods: Of 47 patients who received condoliase, 34 were enrolled in this study. The mean age of the patients was 33 years. The average duration since the onset of disease was 8.6 months. We evaluated patients’ low back and leg pain using a numerical rating scale (NRS) score at two time points (before therapy and 3 months after therapy). We divided the patients into two groups (good group (G): NRS score improvement ≥ 50%, poor group (P): NRS score improvement < 50%). The parameters evaluated were age, disease duration, body mass index (BMI), and positive or negative straight leg raising test results. In addition, the loss of disc height and preoperative radiological findings were evaluated. Results: In terms of low back and leg pain, the G group included 9/34 (26.5%) and 21/34 (61.8%) patients, respectively. Patients’ age (low back pain G/P, 21/36.5 years) was significantly lower in the G group for low back pain (p = 0.001). High-intensity change in the protruded nucleus pulposus (NP) and spinal canal occupancy by the NP ≥ 40% were significantly high in those with leg pain in the G groups (14/21, p = 0.04; and 13/21, p = 0.03, respectively). Conclusions: The efficacy of improvement in leg pain was significantly correlated with high-intensity change and size of the protruded NP. Condoliase was not significantly effective for low back pain but could have an effect on younger patients.

This paper examines the relationship between user pageview (PV) histories and their itemchoice behavior on an e-commerce website. We focus on PV sequences, which represent time series of the number of PVs for each user–item pair. We propose a shape-restricted optimization model that accurately estimates item-choice probabilities for all possible PV sequences. This model imposes monotonicity constraints on item-choice probabilities by exploiting partial orders for PV sequences, according to the recency and frequency of a user’s previous PVs. To improve the computational efficiency of our optimization model, we devise efficient algorithms for eliminating all redundant constraints according to the transitivity of the partial orders. Experimental results using real-world clickstream data demonstrate that our method achieves higher prediction performance than that of a state-of-the-art optimization model and common machine learning methods.