题目4290 · 机器学习
A Fast Sanity Check for Clustering Answers
Why can clustering results vary a lot across random seeds even on the same dataset?
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中文题目题目4289 · 机器学习
Why Hierarchical Clustering Can Be Useful
Why can clustering raw price levels of stocks be misleading compared with clustering normalized returns or features?
打开 →题目2697 · 机器学习
False Winner Probability After Clustering 240 Variants into 24 Families
A researcher generates 240 heavily correlated strategy variants but argues they amount to only 24 effectively independent families. If the desk still flags any family with p-value below 8%, what is the approximate probability of at least one false family-level winner under the nu
打开 →题目4266 · 机器学习
k-Means Assignment Step 1
A point in clustering has average within-cluster distance a=2 and smallest average distance to another cluster b=5. What is its silhouette score?
打开 →题目4281 · 机器学习
Single Linkage Distance 1
For single-linkage hierarchical clustering on 1D points {0,1,4}, which pair merges first?
打开 →模块2.6.4 · 数学与统计能力 · 机器学习理论
无监督学习与强化学习
machine-learning · unsupervised-learning · clustering · k-means · gaussian-mixture-model · em-algorithm · kernel-density-estimation · regime-detection
打开 →模块2.3.2 · 数学与统计能力 · 时间序列分析
波动率与机制转换模型
time-series · volatility · arch · garch · conditional-heteroskedasticity · volatility-clustering · quasi-maximum-likelihood · arch-lm-test
打开 →课程波动率与机制转换模型 · 时间序列分析
ARCH 与 GARCH 模型
某私募(private fund)的风控会上，研究员甩出沪深300 日收益的实证表：日内收益序列本身的自相关系数 公式 在滞后 公式 时几乎全部落在 公式 的 Bartlett 带内；可一旦把同一条序列 平方 再画一次 ACF，从滞后 1 到滞后 60 全是正值、缓慢衰减。再算样本峰度：5.8——远大于正态分布(Gaussian distributi...
打开 →课程无监督学习与强化学习 · 机器学习理论
聚类与密度估计
Hook:5 年沪深300 日收益,你能不能贴出「风险开关」标签 上海某私募的初级量化研究员张昊把过去 5 年的沪深300 日收益拉成一张表——列是 20 日已实现波动率(realized volatility)、申万一级行业截面收益离散度(cross sectional dispersion)、60 日市值加权平均成对相关,1,200 多个交易日。组长甩话...
打开 →题目4283 · 机器学习
Average Linkage Distance 3
A 2D k-means run has centroids at (0,0) and (4,0). For point x=(1,2), which centroid is closer in the assignment step?
打开 →题目4285 · 机器学习
Average Linkage Distance 5
Cluster A has size 3 and mean 0, cluster B has size 1 and mean 2, cluster C has size 1 and mean 5. Under Ward linkage, which pair merges first: A-B or B-C?
打开 →题目4282 · 机器学习
Complete Linkage Distance 2
In DBSCAN with minPts=4, point A has 4 neighbors, point B has 3 neighbors, and B lies within eps of A. What status does B get?
打开 →题目4267 · 机器学习
k-Means Assignment Step 2
A 1D cluster currently contains points [1,2,7]. What centroid does k-means assign to that cluster in the update step?
打开 →题目4268 · 机器学习
k-Means Assignment Step 3
A 2D cluster contains points (0,0), (2,4), and (4,2). What centroid does k-means assign to that cluster?
打开 →题目4269 · 机器学习
k-Means Assignment Step 4
A 2-component GMM has priors 0.6 and 0.4. At point x, the component likelihoods are 0.1 and 0.3. What posterior responsibility does component 2 get?
打开 →题目4270 · 机器学习
k-Means Assignment Step 5
A DBSCAN run uses minPts=5, counting the point itself. A point has 5 neighbors within eps. Is it a core point?
打开 →题目4271 · 机器学习
k-Means Centroid Update 1
In 1D, clusters A={0,2} and B={5,9}. What is their average-linkage distance?
打开 →题目4272 · 机器学习
k-Means Centroid Update 2
A 1D k-means step has current centroids 0 and 10, and the assigned points are {1,2} to the first cluster and {9} to the second. What are the updated centroids?
打开 →题目4273 · 机器学习
k-Means Centroid Update 3
A cluster contains points [1,2,4]. What is its within-cluster SSE around the cluster mean?
打开 →题目4274 · 机器学习
k-Means Centroid Update 4
Under Ward linkage, what merge cost increase do two singleton clusters at positions 1 and 4 have in 1D?
打开 →题目4275 · 机器学习
k-Means Centroid Update 5
Clusters A={1,4} and B={6,8} are compared under complete linkage in 1D. What distance is used?
打开 →题目4284 · 机器学习
Single Linkage Distance 4
In a 2-component GMM with equal priors, component densities at x are 0.12 and 0.08. Which component gets higher responsibility on the first E-step?
打开 →题目4287 · 机器学习
Why k-Means Struggles on Two Moons
Why can k-means behave poorly when one feature has a much larger scale than the others?
打开 →题目4288 · 机器学习
Why Outliers Distort Centroids
Why can silhouette score prefer a smaller k even when larger k lowers SSE?
打开 →题目4286 · 机器学习
Why Scaling Matters for k-Means
You expect non-convex moon-shaped clusters plus some noise points. Would you try k-means or DBSCAN first, and why?
打开 →题目4276 · 机器学习
Within-Cluster Sum of Squares 1
A DBSCAN point has 4 neighbors within eps when minPts=5, so it is not core. If eps is increased and the neighborhood count becomes 6, what status change occurs?
打开 →题目4277 · 机器学习
Within-Cluster Sum of Squares 2
A 1D cluster has members [0,2,4], so its centroid is 2. If an outlier 10 is added to the cluster, by how much does the centroid shift?
打开 →题目4278 · 机器学习
Within-Cluster Sum of Squares 3
A point has silhouette inputs a=3 and b=5. If b falls to 4 while a stays fixed, how much does the silhouette score decrease?
打开 →题目4279 · 机器学习
Within-Cluster Sum of Squares 4
In a 2-component GMM with equal priors, component 1 has likelihood 0.2 at x while component 2 has likelihood 0.1, so responsibility_1 is 2/3. If component 2's likelihood rises to 0.2, what does responsibility_1 become?
打开 →题目4280 · 机器学习
Within-Cluster Sum of Squares 5
The Euclidean distance between (0,0) and (3,40) is computed on raw features. If the second feature is standardized by dividing it by 10 while the first is unchanged, what new distance do you get?
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