機械学習英語150(日記)


### 1. **Supervised learning**

**Example**: The data analyst used supervised learning to predict future sales based on historical transaction records.
**Explanation**: Supervised learning requires labeled data and is widely used in forecasting and classification tasks in business.

### 2. **Unsupervised learning**

**Example**: The marketing team applied unsupervised learning to group customers with similar purchasing behavior.
**Explanation**: This approach identifies hidden patterns without pre-labeled outcomes, ideal for segmentation and discovery.

### 3. **Reinforcement learning**

**Example**: Our robotics division is experimenting with reinforcement learning to optimize warehouse automation.
**Explanation**: It allows agents to learn optimal actions by receiving rewards from the environment, often used in control systems.

### 4. **Deep learning**

**Example**: The IT department implemented deep learning techniques to improve image recognition accuracy.
**Explanation**: Deep learning uses multiple neural network layers to extract high-level features, useful in processing complex data like images and audio.

### 5. **Neural network**

**Example**: The engineer designed a neural network to classify documents based on their content.
**Explanation**: A neural network mimics the human brain structure and is the foundation of many machine learning applications.

### 6. **Convolutional neural network (CNN)**

**Example**: CNNs are especially effective for identifying patterns in images, such as defects in product photos.
**Explanation**: CNNs are a type of deep learning model optimized for image and spatial data, often used in manufacturing and surveillance.

### 7. **Recurrent neural network (RNN)**

**Example**: The company used an RNN to analyze customer reviews and track sentiment changes over time.
**Explanation**: RNNs are designed to handle sequential data like time series or text, making them ideal for trend analysis.

### 8. **Long Short-Term Memory (LSTM)**

**Example**: LSTM models help forecast monthly revenue by capturing long-term dependencies in the data.
**Explanation**: LSTM is an advanced RNN that preserves memory over long sequences, reducing vanishing gradient problems.

### 9. **Transformer**

**Example**: The translation tool is powered by a transformer model that can process entire sentences at once.
**Explanation**: Transformers outperform RNNs in many natural language processing tasks by leveraging self-attention mechanisms.

### 10. **Self-attention mechanism**

**Example**: By using self-attention, the model focused on the most relevant words in a customer support inquiry.
**Explanation**: Self-attention calculates the importance of each part of a sequence, enabling the model to weigh context effectively.


### 11. **Pretraining（事前学習）**

**Example**: The language model was pretrained on a large dataset before being fine-tuned for legal document classification.
**Explanation**: Pretraining allows models to learn general features from massive datasets, which boosts performance when adapted to specific tasks.

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### 12. **Transfer learning（転移学習）**

**Example**: Our development team applied transfer learning to reduce the time needed to train the new image classifier.
**Explanation**: Transfer learning enables reuse of knowledge from one task in a new but related problem, reducing data and computation costs.

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### 13. **Self-supervised learning（自己教師あり学習）**

**Example**: The research unit explored self-supervised learning methods to improve the system’s understanding of customer emails.
**Explanation**: Self-supervised learning uses unlabeled data to generate its own supervisory signals, useful in natural language and vision tasks.

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### 14. **Generative model（生成モデル）**

**Example**: The design tool uses a generative model to suggest new product prototypes based on past designs.
**Explanation**: A generative model learns the distribution of data and can generate new samples, often used in design, art, or simulation.

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### 15. **Generative Adversarial Network (GAN)（生成的敵対ネットワーク）**

**Example**: The company employed a GAN to generate realistic synthetic faces for avatar customization.
**Explanation**: GANs consist of a generator and a discriminator competing in a zero-sum game, producing highly realistic outputs.

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### 16. **Autoencoder（オートエンコーダ）**

**Example**: Autoencoders were implemented to compress and reconstruct customer data for storage efficiency.
**Explanation**: An autoencoder is a neural network used for unsupervised feature learning and dimensionality reduction.

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### 17. **Bayesian learning（ベイズ学習）**

**Example**: Bayesian learning was adopted to update risk predictions as new market data arrived.
**Explanation**: Bayesian methods incorporate prior beliefs and update probabilities as evidence accumulates, making them ideal for uncertainty modeling.

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### 18. **Overfitting（過学習）**

**Example**: The initial model showed signs of overfitting, performing well on training data but poorly on unseen cases.
**Explanation**: Overfitting occurs when a model learns noise in training data and fails to generalize to new data.

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### 19. **Underfitting（未学習）**

**Example**: The basic model underfit the data, failing to capture any meaningful trends in customer activity.
**Explanation**: Underfitting happens when a model is too simple, lacking the capacity to learn the underlying structure of the data.

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### 20. **Generalization performance（汎化性能）**

**Example**: We selected the model with the best generalization performance on the validation dataset.
**Explanation**: Generalization performance reflects how well a model performs on unseen data and is critical for real-world applications.


### 21. **Learning rate（学習率）**

**Example**: Adjusting the learning rate helped the model converge more efficiently during training.
**Explanation**: The learning rate controls how much a model's parameters change with each update. A rate that’s too high can cause instability, while one that’s too low may slow down training.

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### 22. **Batch size（バッチサイズ）**

**Example**: Reducing the batch size improved the model’s performance on limited hardware.
**Explanation**: Batch size determines how many training samples are processed at once. It affects memory usage and training dynamics.

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### 23. **Epoch（エポック）**

**Example**: After 50 epochs, the model began to overfit the training data.
**Explanation**: An epoch is one complete pass through the entire training dataset. More epochs can improve accuracy, but too many may lead to overfitting.

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### 24. **Mini-batch learning（ミニバッチ学習）**

**Example**: Mini-batch learning balances the efficiency of batch processing with the noise reduction of stochastic methods.
**Explanation**: Instead of updating the model after every sample or the whole dataset, mini-batch learning updates it after a small subset of samples.

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### 25. **Logistic regression（ロジスティック回帰）**

**Example**: The HR department used logistic regression to predict employee retention.
**Explanation**: Logistic regression models the probability of binary outcomes and is widely used in classification tasks like churn prediction.

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### 26. **Linear regression（線形回帰）**

**Example**: We applied linear regression to estimate the monthly impact of marketing spend on sales.
**Explanation**: Linear regression predicts a continuous output by modeling a linear relationship between input variables and the target.

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### 27. **Decision tree（決定木）**

**Example**: A decision tree was used to map out the factors leading to customer cancellations.
**Explanation**: Decision trees split data into branches based on feature thresholds, making them easy to interpret and visualize.

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### 28. **Random forest（ランダムフォレスト）**

**Example**: The random forest model outperformed others in identifying fraudulent transactions.
**Explanation**: A random forest is an ensemble of decision trees that improves prediction accuracy and reduces overfitting.

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### 29. **Support Vector Machine (SVM)（サポートベクターマシン）**

**Example**: The team implemented an SVM to classify emails as spam or legitimate.
**Explanation**: SVMs find the optimal hyperplane to separate classes, especially effective in high-dimensional spaces.

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### 30. **K-nearest neighbors (KNN)（k近傍法）**

**Example**: KNN was used to recommend similar products to online shoppers.
**Explanation**: KNN classifies a sample based on the majority label of its closest neighbors. It is simple and effective for recommendation systems and pattern recognition.

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### 31. **Principal Component Analysis (PCA)（主成分分析）**

**Example**: We used PCA to reduce the dimensionality of the customer data before visualization.
**Explanation**: PCA is a linear technique for reducing the number of variables by projecting data onto its principal components, often used to simplify complex datasets.

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### 32. **Singular Value Decomposition (SVD)（特異値分解）**

**Example**: SVD was applied in the recommendation engine to identify latent factors in user preferences.
**Explanation**: SVD decomposes a matrix into singular vectors and values, useful in compression, recommendation, and noise reduction tasks.

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### 33. **Clustering（クラスタリング）**

**Example**: The marketing team used clustering to group similar customers based on shopping behavior.
**Explanation**: Clustering algorithms divide data into groups where points in the same group are more similar to each other than to those in other groups.

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### 34. **K-means（k平均法）**

**Example**: K-means clustering helped us identify distinct segments among website visitors.
**Explanation**: K-means partitions data into k clusters by minimizing the within-cluster variance, commonly used in customer segmentation and behavior analysis.

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### 35. **Hierarchical clustering（階層的クラスタリング）**

**Example**: Hierarchical clustering provided a tree-like view of product similarity.
**Explanation**: This method builds a hierarchy of clusters using either agglomerative (bottom-up) or divisive (top-down) approaches, useful for exploratory data analysis.

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### 36. **DBSCAN**

**Example**: We used DBSCAN to detect abnormal user activity that didn’t fit typical patterns.
**Explanation**: DBSCAN is a density-based clustering algorithm that identifies outliers and arbitrary-shaped clusters, effective for anomaly detection.

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### 37. **Topic model（トピックモデル）**

**Example**: The topic model uncovered key themes in thousands of customer reviews.
**Explanation**: Topic models analyze documents to discover latent topics based on word distributions, useful for text summarization and search.

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### 38. **Latent Dirichlet Allocation (LDA)（潜在ディリクレ配分法）**

**Example**: We applied LDA to categorize support tickets by topic without manual labeling.
**Explanation**: LDA is a generative probabilistic model that assigns topics to documents using a Dirichlet distribution, widely used in natural language processing.

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### 39. **Gradient boosting（勾配ブースティング）**

**Example**: Gradient boosting significantly improved our model’s prediction accuracy for loan defaults.
**Explanation**: Gradient boosting builds a strong learner by sequentially adding models that correct the previous model’s errors, commonly used in structured data tasks.

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### 40. **XGBoost**

**Example**: XGBoost outperformed other models in our Kaggle competition submission.
**Explanation**: XGBoost is a highly efficient and regularized implementation of gradient boosting, often winning machine learning competitions for its speed and accuracy.

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### 41. **LightGBM**

**Example**: LightGBM reduced our training time while maintaining high model accuracy.
**Explanation**: LightGBM is a gradient boosting framework developed by Microsoft, optimized for speed and memory efficiency, particularly in large datasets.

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### 42. **CatBoost**

**Example**: CatBoost performed better on categorical features compared to other boosting methods.
**Explanation**: CatBoost is a gradient boosting algorithm developed by Yandex that handles categorical variables natively and prevents overfitting.

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### 43. **Ensemble learning（アンサンブル学習）**

**Example**: Ensemble learning improved our model's robustness by combining predictions from multiple algorithms.
**Explanation**: Ensemble methods like bagging, boosting, and stacking aggregate outputs from several models to improve overall performance and stability.

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### 44. **Bagging（バギング）**

**Example**: We used bagging to reduce variance and prevent overfitting in our decision tree model.
**Explanation**: Bagging (Bootstrap Aggregating) creates multiple subsets of data, trains a model on each, and combines their outputs to stabilize predictions.

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### 45. **Boosting（ブースティング）**

**Example**: Boosting was used to incrementally improve the model by focusing on the mistakes of previous models.
**Explanation**: Boosting is a sequential ensemble technique that prioritizes learning from errors in previous iterations, increasing overall accuracy.

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### 46. **Stacking（スタッキング）**

**Example**: Stacking enabled us to blend several models and achieve better prediction on the validation set.
**Explanation**: Stacking combines outputs from multiple base models using a meta-model, leveraging diverse model strengths for improved performance.

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### 47. **Hyperparameter（ハイパーパラメータ）**

**Example**: Tuning the hyperparameters significantly improved the model’s F1-score.
**Explanation**: Hyperparameters are configuration settings set before training (e.g., learning rate, tree depth), which affect how the model learns.

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### 48. **Grid search（グリッドサーチ）**

**Example**: We performed grid search to identify the optimal combination of model hyperparameters.
**Explanation**: Grid search exhaustively tests all combinations of specified hyperparameters to find the best performing setup.

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### 49. **Random search（ランダムサーチ）**

**Example**: Random search provided faster results than grid search with comparable accuracy.
**Explanation**: Random search samples combinations randomly from the hyperparameter space, often more efficient than grid search in high dimensions.

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### 50. **Bayesian optimization（ベイズ最適化）**

**Example**: Bayesian optimization helped us find the best hyperparameters using fewer trials.
**Explanation**: Bayesian optimization builds a probabilistic model of the objective function and selects promising configurations, useful for expensive evaluations.





### 51. **Accuracy（精度）**

**Example**: The accuracy of the model was over 95%, but it failed to detect rare cases.
**Explanation**: Accuracy is the ratio of correct predictions to total predictions, but it can be misleading for imbalanced datasets.

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### 52. **Precision（適合率）**

**Example**: We focused on precision to minimize false positives in fraud detection.
**Explanation**: Precision measures how many of the predicted positives are actually correct, important in high-risk applications like finance and healthcare.

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### 53. **Recall（再現率）**

**Example**: Recall improved after we adjusted the decision threshold.
**Explanation**: Recall measures the proportion of actual positives that were correctly identified, useful when missing positive cases is costly.

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### 54. **F1 score（F1スコア）**

**Example**: We optimized the F1 score to balance precision and recall in the classification task.
**Explanation**: The F1 score is the harmonic mean of precision and recall, offering a single metric that balances both.

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### 55. **Confusion matrix（混同行列）**

**Example**: The confusion matrix showed a high number of false negatives, indicating a recall problem.
**Explanation**: A confusion matrix is a summary of prediction results showing true/false positives and negatives, helping analyze classification performance.

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### 56. **True positive (TP)（真陽性）**

**Example**: Increasing true positives without raising false positives improved model reliability.
**Explanation**: True positives are correctly predicted positive cases and indicate successful detection in classification.

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### 57. **False positive (FP)（偽陽性）**

**Example**: Too many false positives caused unnecessary alerts in the security system.
**Explanation**: A false positive occurs when the model incorrectly classifies a negative case as positive, potentially wasting resources.

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### 58. **True negative (TN)（真陰性）**

**Example**: True negatives indicate that the model correctly identified safe transactions.
**Explanation**: True negatives are correct predictions of negative cases, crucial in models that aim to detect anomalies.

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### 59. **False negative (FN)（偽陰性）**

**Example**: False negatives in medical diagnoses can lead to dangerous outcomes.
**Explanation**: A false negative occurs when a positive case is missed, and is often more serious than false positives depending on the context.

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### 60. **ROC curve（ROC曲線）**

**Example**: We used the ROC curve to evaluate the trade-off between sensitivity and specificity.
**Explanation**: The ROC curve plots true positive rate against false positive rate at various thresholds, visualizing classification performance.

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### 61. **AUC（Area Under Curve）**

**Example**: The model with the highest AUC was selected for production deployment.
**Explanation**: AUC measures the area under the ROC curve and reflects a model’s ability to distinguish between classes across all thresholds.

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### 62. **Loss function（損失関数）**

**Example**: Choosing the right loss function helped align the model with our business goals.
**Explanation**: A loss function quantifies how far off predictions are from actual values, guiding the optimization during training.

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### 63. **Squared error（二乗誤差）**

**Example**: The squared error was used to penalize large deviations in the regression model.
**Explanation**: Squared error is the square of the difference between predicted and actual values, emphasizing large errors.

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### 64. **Mean Squared Error (MSE)（平均二乗誤差）**

**Example**: MSE was the primary evaluation metric for our housing price prediction model.
**Explanation**: MSE is the average of squared errors, widely used in regression to assess prediction accuracy.

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### 65. **Mean Absolute Error (MAE)（平均絶対誤差）**

**Example**: MAE gave us a more interpretable measure of average prediction error in dollars.
**Explanation**: MAE is the average of absolute errors, offering a straightforward measure of prediction deviation.

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### 66. **Cross-entropy（クロスエントロピー）**

**Example**: The cross-entropy loss was minimized during classification model training.
**Explanation**: Cross-entropy measures the difference between predicted and true probability distributions, often used in classification tasks.

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### 67. **Gradient of the loss（ロスの勾配）**

**Example**: The gradient of the loss guides how the model's parameters should be updated.
**Explanation**: The gradient is the derivative of the loss function with respect to model parameters, essential for optimization algorithms like gradient descent.

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### 68. **Bias（バイアス）**

**Example**: High bias led the model to oversimplify the relationships in the data.
**Explanation**: Bias refers to errors from incorrect assumptions in the learning algorithm, which can lead to underfitting.

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### 69. **Variance（バリアンス）**

**Example**: Reducing model variance helped improve stability across datasets.
**Explanation**: Variance measures how much a model’s predictions change with different training data; high variance often leads to overfitting.

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### 70. **Bias-variance trade-off（バイアス-バリアンストレードオフ）**

**Example**: We adjusted the model complexity to find a better bias-variance trade-off.
**Explanation**: This trade-off represents the balance between underfitting (high bias) and overfitting (high variance).

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### 71. **Model selection（モデル選択）**

**Example**: Model selection was based on validation accuracy and computational cost.
**Explanation**: Model selection is the process of choosing the best-performing model from a set of candidates based on evaluation metrics.

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### 72. **Model evaluation（モデル評価）**

**Example**: We performed model evaluation using multiple metrics before deployment.
**Explanation**: Model evaluation assesses how well a model performs, often using metrics like precision, recall, or AUC.

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### 73. **Holdout validation（ホールドアウト検証）**

**Example**: Holdout validation was used to simulate how the model would perform on new data.
**Explanation**: The dataset is split into training and test sets to evaluate generalization performance without cross-validation.

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### 74. **Cross-validation（クロスバリデーション）**

**Example**: Cross-validation gave us a more reliable estimate of model performance.
**Explanation**: In cross-validation, the dataset is split into multiple folds to train and test the model repeatedly, reducing the risk of overfitting.

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### 75. **K-fold cross-validation（k分割交差検証）**

**Example**: We used 5-fold cross-validation to assess model consistency across different data subsets.
**Explanation**: The data is divided into k parts; the model is trained on k-1 parts and validated on the remaining one, rotating through all folds.

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### 76. **Optimization problem（最適化問題）**

**Example**: Training a machine learning model is essentially an optimization problem.
**Explanation**: In machine learning, optimization problems aim to minimize (or maximize) an objective function, often related to prediction error.

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### 77. **Gradient descent（勾配降下法）**

**Example**: We used gradient descent to minimize the model’s loss function efficiently.
**Explanation**: Gradient descent updates model parameters in the direction of steepest decrease in the loss function, guiding learning.

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### 78. **Stochastic Gradient Descent (SGD)（確率的勾配降下法）**

**Example**: SGD was chosen for faster convergence on large datasets.
**Explanation**: SGD updates parameters using one or a few samples at a time, offering efficiency and noise that can help escape local minima.

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### 79. **Mini-batch SGD（ミニバッチSGD）**

**Example**: Mini-batch SGD achieved a balance between speed and stability.
**Explanation**: Instead of one sample or the whole dataset, mini-batch SGD uses small random subsets for training updates.

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### 80. **Momentum（モーメンタム）**

**Example**: Momentum helped the model move past small local minima during training.
**Explanation**: Momentum accumulates gradients to maintain direction during updates, accelerating convergence and smoothing the optimization path.

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### 81. **RMSProp**

**Example**: RMSProp was used to adapt the learning rate dynamically during optimization.
**Explanation**: RMSProp adjusts the learning rate for each parameter by dividing by a running average of recent gradients, improving training on non-stationary data.

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### 82. **Adam**

**Example**: The Adam optimizer led to faster and more stable convergence.
**Explanation**: Adam combines momentum and adaptive learning rates, and is widely used for deep learning due to its robustness and efficiency.

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### 83. **AdaGrad**

**Example**: AdaGrad was effective for handling sparse features in the recommendation system.
**Explanation**: AdaGrad adapts learning rates based on past gradient information, performing well when some features are infrequently updated.

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### 84. **Learning rate scheduling（学習率スケジューリング）**

**Example**: We applied learning rate scheduling to fine-tune the model in later training stages.
**Explanation**: Learning rate scheduling adjusts the rate over time, often reducing it as training progresses to allow for fine convergence.

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### 85. **Weight decay（重み減衰）**

**Example**: Weight decay helped regularize the model and prevent overfitting.
**Explanation**: Weight decay adds a penalty to large weights in the loss function, promoting simpler models that generalize better.

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### 86. **Regularization（正則化）**

**Example**: Regularization was necessary to maintain generalization across different datasets.
**Explanation**: Regularization adds constraints to the loss function to prevent the model from fitting noise in the training data.

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### 87. **L1 regularization（L1正則化）**

**Example**: We used L1 regularization to reduce the number of active features.
**Explanation**: L1 adds a penalty proportional to the absolute value of weights, encouraging sparsity in the model.

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### 88. **L2 regularization（L2正則化）**

**Example**: L2 regularization helped maintain weight balance and avoid overfitting.
**Explanation**: L2 penalizes the square of weights, leading to more stable and smooth models without eliminating features entirely.

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### 89. **Dropout**

**Example**: Dropout was applied to the hidden layers to prevent overfitting in the neural network.
**Explanation**: Dropout randomly disables neurons during training to prevent co-dependence and improve generalization.

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### 90. **Batch normalization（バッチ正規化）**

**Example**: Batch normalization improved training speed and model stability.
**Explanation**: Batch normalization normalizes inputs of each layer to reduce internal covariate shift, accelerating training and improving performance.


### 91. **Early stopping（早期終了）**

**Example**: We applied early stopping to halt training once the validation loss began to increase.
**Explanation**: Early stopping stops model training when performance on a validation set starts to degrade, preventing overfitting.

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### 92. **Vanishing gradient（勾配消失）**

**Example**: The team faced a vanishing gradient problem when training deep networks with sigmoid activation.
**Explanation**: Vanishing gradients occur when gradients become too small during backpropagation, slowing or halting learning in deep networks.

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### 93. **Exploding gradient（勾配爆発）**

**Example**: We clipped the gradients to resolve the exploding gradient issue in the RNN.
**Explanation**: Exploding gradients happen when gradients become excessively large, destabilizing training and causing numerical errors.

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### 94. **Activation function（活性化関数）**

**Example**: Choosing the right activation function is critical for non-linear transformations in neural networks.
**Explanation**: Activation functions introduce non-linearity into neural networks, enabling them to learn complex patterns.

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### 95. **Sigmoid function（シグモイド関数）**

**Example**: The sigmoid function was used in the output layer for binary classification.
**Explanation**: The sigmoid squashes input values into a \[0, 1] range and is often used when probabilities are needed as output.

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### 96. **Tanh function（tanh関数）**

**Example**: Tanh activation was preferred over sigmoid due to its zero-centered output.
**Explanation**: The tanh function maps inputs to \[–1, 1], improving convergence by producing outputs centered around zero.

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### 97. **ReLU（Rectified Linear Unit）**

**Example**: ReLU is widely used in deep networks for its simplicity and computational efficiency.
**Explanation**: ReLU outputs zero for negative inputs and linear values for positive ones, helping mitigate vanishing gradients.

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### 98. **Leaky ReLU**

**Example**: Leaky ReLU prevented dead neurons by allowing small gradients when inputs were negative.
**Explanation**: Leaky ReLU modifies ReLU to allow a small, non-zero gradient for negative inputs, improving training dynamics.

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### 99. **Softmax function（ソフトマックス関数）**

**Example**: We used the softmax function to convert raw scores into class probabilities.
**Explanation**: Softmax transforms a vector into a probability distribution over classes, commonly used in multiclass classification.

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### 100. **Softmax classifier（ソフトマックス分類器）**

**Example**: The softmax classifier helped us determine the most likely category for each document.
**Explanation**: A softmax classifier uses the softmax function to assign class probabilities and selects the class with the highest score.

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### 101. **Scalar（スカラー）**

**Example**: A scalar represents a single numerical value, often used for learning rates.
**Explanation**: In linear algebra, a scalar is a single number that can scale vectors and matrices.

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### 102. **Vector（ベクトル）**

**Example**: Each customer profile was converted into a feature vector for analysis.
**Explanation**: A vector is an ordered list of numbers, commonly used to represent data points or weights in machine learning models.

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### 103. **Matrix（行列）**

**Example**: The image data was stored in a matrix of pixel values.
**Explanation**: A matrix is a 2D array of numbers used for transformations, inputs, and operations in machine learning.

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### 104. **Tensor（テンソル）**

**Example**: The model was trained using multi-dimensional tensors for input and output.
**Explanation**: A tensor is a generalization of vectors and matrices to more dimensions, used extensively in deep learning frameworks.

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### 105. **Transpose matrix（転置行列）**

**Example**: We transposed the matrix to align feature dimensions for multiplication.
**Explanation**: A transposed matrix flips its rows and columns, often needed for compatibility in operations.

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### 106. **Identity matrix（単位行列）**

**Example**: Multiplying by the identity matrix left the vector unchanged.
**Explanation**: An identity matrix has 1s on the diagonal and 0s elsewhere, acting as a multiplicative identity in matrix algebra.

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### 107. **Inverse matrix（逆行列）**

**Example**: The inverse matrix was used to solve the system of linear equations.
**Explanation**: An inverse matrix reverses the effect of another matrix, and is key to solving matrix equations analytically.

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### 108. **Matrix multiplication（行列の積）**

**Example**: Matrix multiplication is essential for propagating data through neural networks.
**Explanation**: This operation combines two matrices according to specific algebraic rules, central to linear transformations.

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### 109. **Hadamard product（アダマール積）**

**Example**: The Hadamard product was applied element-wise to combine two matrices.
**Explanation**: This is the element-wise product of two matrices of the same shape, used in some neural network computations.

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### 110. **Inner product（内積）**

**Example**: We computed the inner product to measure similarity between two user vectors.
**Explanation**: The inner product (dot product) is a scalar result that quantifies alignment between two vectors.

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### 111. **Outer product（外積）**

**Example**: The outer product formed a matrix from two vectors for attention mechanisms.
**Explanation**: The outer product takes two vectors and produces a matrix, used in tensor operations and model representations.

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### 112. **Norm（ノルム）**

**Example**: The L2 norm was used to penalize large weights in the model.
**Explanation**: A norm measures the size or length of a vector, useful for regularization and optimization.

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### 113. **Euclidean distance（ユークリッド距離）**

**Example**: We used Euclidean distance to find the nearest neighbors in the feature space.
**Explanation**: It is the straight-line distance between two points, widely used for clustering and recommendation.

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### 114. **Cosine similarity（コサイン類似度）**

**Example**: Cosine similarity was used to recommend products based on customer behavior.
**Explanation**: Cosine similarity measures the angle between vectors, often preferred when magnitude is less important than direction.

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### 115. **Eigenvalue（固有値）**

**Example**: Eigenvalues helped us understand the variance captured by each principal component.
**Explanation**: Eigenvalues represent the magnitude of scaling along a direction, fundamental in PCA and SVD.

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### 116. **Eigenvector（固有ベクトル）**

**Example**: Each eigenvector pointed to a principal axis of the data’s variance.
**Explanation**: Eigenvectors show directions in which transformations stretch data, paired with eigenvalues in matrix decompositions.

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### 117. **Linear independence（線形独立）**

**Example**: We checked for linear independence to ensure feature uniqueness.
**Explanation**: Vectors are linearly independent if no vector can be written as a combination of others, ensuring no redundancy in data.

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### 118. **Rank（ランク）**

**Example**: The matrix’s rank determined the number of useful features in the dataset.
**Explanation**: Rank is the number of linearly independent rows or columns in a matrix, revealing its dimensional capacity.

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### 119. **Singular value（特異値）**

**Example**: The largest singular values indicated dominant patterns in the dataset.
**Explanation**: Singular values represent the magnitude of principal directions in matrix data, key to dimensionality reduction.

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### 120. **Singular Value Decomposition (SVD)（特異値分解）**

**Example**: SVD was used to compress the image dataset while preserving key features.
**Explanation**: SVD breaks a matrix into three components, revealing its structure and enabling compression, noise reduction, and more.

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### 121. **Random variable（確率変数）**

**Example**: The model treated customer age as a random variable in its prediction.
**Explanation**: A random variable assigns numerical outcomes to random events, essential in probabilistic modeling.

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### 122. **Probability distribution（確率分布）**

**Example**: We assumed a normal probability distribution for delivery times.
**Explanation**: A probability distribution describes the likelihood of various outcomes for a random variable.

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### 123. **Uniform distribution（一様分布）**

**Example**: The system sampled from a uniform distribution to initialize weights randomly.
**Explanation**: In a uniform distribution, all outcomes have equal probability—often used in simulations and initialization.

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### 124. **Normal distribution（正規分布）**

**Example**: Customer satisfaction scores followed a normal distribution.
**Explanation**: A bell-shaped distribution where most values cluster around the mean—widely used in statistical inference.

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### 125. **Bernoulli distribution（ベルヌーイ分布）**

**Example**: The Bernoulli distribution modeled whether a user clicked an ad or not.
**Explanation**: This distribution handles binary outcomes like success/failure, yes/no, used in classification tasks.

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### 126. **Binomial distribution（二項分布）**

**Example**: We used a binomial distribution to estimate click-through rates over multiple trials.
**Explanation**: The binomial distribution models the number of successes in a fixed number of binary trials.

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### 127. **Poisson distribution（ポアソン分布）**

**Example**: Customer service calls per hour were modeled using a Poisson distribution.
**Explanation**: This distribution describes the number of events occurring in a fixed interval, often used in queuing theory.

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### 128. **Exponential distribution（指数分布）**

**Example**: The time between failures in our system was modeled by an exponential distribution.
**Explanation**: The exponential distribution is used to model the time between events in a Poisson process.

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### 129. **Conditional probability（条件付き確率）**

**Example**: Conditional probability helped us estimate repeat purchases given a prior order.
**Explanation**: It is the probability of an event occurring given that another event has already occurred.

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### 130. **Joint probability（同時確率）**

**Example**: The joint probability of age and income was used to build the customer profile.
**Explanation**: It refers to the likelihood of two events happening at the same time.

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### 131. **Marginal probability（周辺確率）**

**Example**: The marginal probability of churn was calculated across all customer segments.
**Explanation**: This is the probability of a single event irrespective of the outcome of other variables.

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### 132. **Bayes’ theorem（ベイズの定理）**

**Example**: We used Bayes’ theorem to update the likelihood of fraud after new evidence.
**Explanation**: Bayes’ theorem reverses conditional probabilities and is used for updating beliefs based on data.

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### 133. **Likelihood（尤度）**

**Example**: The model’s parameters were adjusted to maximize likelihood.
**Explanation**: Likelihood measures how probable the observed data is, given a specific model configuration.

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### 134. **Posterior probability（事後確率）**

**Example**: The spam filter calculates posterior probability to determine email classification.
**Explanation**: This is the updated probability of a hypothesis after observing data, central to Bayesian inference.

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### 135. **Expected value（期待値）**

**Example**: The expected value of revenue per user was calculated for investment decisions.
**Explanation**: This is the average outcome of a random variable over many trials, used in planning and forecasting.

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### 136. **Variance（分散）**

**Example**: High variance in delivery times signaled an issue in the logistics chain.
**Explanation**: Variance measures how spread out values are from the mean—important in risk assessment.

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### 137. **Covariance（共分散）**

**Example**: Covariance between advertising and sales helped assess campaign effectiveness.
**Explanation**: It indicates the directional relationship between two variables.

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### 138. **Correlation coefficient（相関係数）**

**Example**: A high correlation coefficient was observed between temperature and energy usage.
**Explanation**: This normalized measure (–1 to 1) quantifies the strength and direction of a linear relationship.

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### 139. **Shannon entropy（シャノンエントロピー）**

**Example**: We measured entropy to quantify the uncertainty in customer behavior.
**Explanation**: Entropy measures the average uncertainty or information content in a probability distribution.

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### 140. **KL divergence（KLダイバージェンス）**

**Example**: KL divergence was minimized to match the model’s distribution to the real data.
**Explanation**: This measures how one probability distribution diverges from a reference distribution.

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### 141. **Information gain（情報利得）**

**Example**: The feature with the highest information gain was chosen as the root node.
**Explanation**: Information gain quantifies how much a feature reduces uncertainty in decision trees.

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### 142. **Maximum likelihood estimation（最尤推定）**

**Example**: We applied maximum likelihood estimation to determine the model parameters.
**Explanation**: MLE finds parameters that maximize the probability of observing the given data.

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### 143. **Bayesian estimation（ベイズ推定）**

**Example**: Bayesian estimation allowed us to incorporate prior knowledge into the model.
**Explanation**: This method combines prior beliefs with observed data to update parameter estimates.

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### 144. **Statistical hypothesis testing（統計的仮説検定）**

**Example**: We conducted hypothesis testing to validate the marketing campaign’s effect.
**Explanation**: Hypothesis testing determines whether observed effects are statistically significant.

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### 145. **p-value（p値）**

**Example**: A p-value below 0.05 indicated that the result was statistically significant.
**Explanation**: The p-value represents the probability of observing the data if the null hypothesis were true.

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### 146. **Null hypothesis（帰無仮説）**

**Example**: We failed to reject the null hypothesis, suggesting no difference between groups.
**Explanation**: The null hypothesis is a default assumption of no effect or no difference, tested in statistical analysis.

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### 147. **Alternative hypothesis（対立仮説）**

**Example**: The alternative hypothesis claimed that the new strategy increased sales.
**Explanation**: This hypothesis represents the effect or difference researchers aim to support.

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### 148. **Significance level（有意水準）**

**Example**: We set the significance level at 0.01 to reduce false positives.
**Explanation**: It defines the threshold for rejecting the null hypothesis, commonly set at 0.05.

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### 149. **t-test（t検定）**

**Example**: A t-test was performed to compare conversion rates between two landing pages.
**Explanation**: The t-test assesses whether the means of two groups are statistically different.

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### 150. **Chi-square test（カイ二乗検定）**

**Example**: The chi-square test confirmed a significant association between age and purchase behavior.
**Explanation**: This test evaluates relationships between categorical variables, useful in survey and marketing analysis.

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