{"id":1195,"date":"2023-07-27T08:09:52","date_gmt":"2023-07-27T08:09:52","guid":{"rendered":"https:\/\/statorials.org\/my\/lasso-%e1%80%86%e1%80%af%e1%80%90%e1%80%ba%e1%80%9a%e1%80%af%e1%80%90%e1%80%ba%e1%80%99%e1%80%be%e1%80%af\/"},"modified":"2023-07-27T08:09:52","modified_gmt":"2023-07-27T08:09:52","slug":"lasso-%e1%80%86%e1%80%af%e1%80%90%e1%80%ba%e1%80%9a%e1%80%af%e1%80%90%e1%80%ba%e1%80%99%e1%80%be%e1%80%af","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/lasso-%e1%80%86%e1%80%af%e1%80%90%e1%80%ba%e1%80%9a%e1%80%af%e1%80%90%e1%80%ba%e1%80%99%e1%80%be%e1%80%af\/","title":{"rendered":"Lasso regression \u1014\u102d\u1012\u102b\u1014\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u101e\u102c\u1019\u102c\u1014\u103a <a href=\"https:\/\/statorials.org\/my\/multiple-linear-regression\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1019\u103b\u102d\u102f\u1038\u1005\u102f\u1036\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f<\/a> \u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u104f\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a <em>p<\/em> \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a <a href=\"https:\/\/statorials.org\/my\/\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c-\u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a-\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/a> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X <sub>1<\/sub> <sub>+<\/sub> \u03b2 <sub>2<\/sub> X <sub>2<\/sub> + \u2026 + \u03b2 <sub>p<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Y<\/strong> : \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>X <sub>j<\/sub><\/strong> : j <sup>th<\/sup> \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03b2 <sub>j<\/sub><\/strong> : X <sub>j<\/sub> \u1010\u103d\u1004\u103a \u1010\u1005\u103a\u101a\u1030\u1014\u1005\u103a\u1010\u102d\u102f\u1038\u101c\u102c\u1019\u103e\u102f\u104f Y \u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1001\u103c\u102c\u1038\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u101e\u1031\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u100a\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03b5<\/strong> : \u1021\u1019\u103e\u102c\u1038\u1021\u101a\u103d\u1004\u103a\u1038 \u1000\u102d\u1014\u103a\u1038<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u03b2 <sub>0<\/sub> , \u03b2 <sub>1<\/sub> , B <sub>2<\/sub> , \u2026, \u03b2 <sub>p<\/sub> \u104f \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 (RSS) \u104f \u1014\u103e\u1005\u103a\u1011\u1015\u103a\u1000\u102d\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1005\u1031\u101e\u100a\u1037\u103a <strong>\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038 \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1015\u102f\u1036\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS = \u03a3(y <sub>i<\/sub> \u2013 \u0177 <sub>i<\/sub> ) <sup>\u1042<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u2211<\/strong> : <em>\u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1012\u103a<\/em> \u101f\u102f \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u101b\u101e\u1031\u102c \u1002\u101b\u102d\u101e\u1004\u103a\u1039\u1000\u1031\u1010<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : <sup>\u1021\u102d\u102f\u1004\u103a\u1010\u102e<\/sup> \u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u1019\u103e\u1014\u103a\u1010\u1000\u101a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1010\u1014\u103a\u1016\u102d\u102f\u1038<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : Multiple linear regression model \u1000\u102d\u102f \u1021\u1001\u103c\u1031\u1001\u1036\u104d \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1010\u1014\u103a\u1016\u102d\u102f\u1038<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101b\u102c\u1010\u103d\u1004\u103a\u104a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1014\u1031\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a\u104a <a href=\"https:\/\/statorials.org\/my\/multicollinearity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1000\u1031\u102c\u103a\u101c\u102d\u102f\u1004\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u102f\u1036\u101e\u100a\u103a<\/a> \u1015\u103c\u103f\u1014\u102c\u1016\u103c\u1005\u103a\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1016\u1031\u102c\u103a\u1000\u102d\u1014\u103a\u1038 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1005\u102d\u1010\u103a\u1001\u103b\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u1005\u1031\u1018\u1032 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1015\u103c\u101e\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f \u101a\u1001\u1004\u103a\u1000 \u1010\u1005\u103a\u1001\u102b\u1019\u103e\u1019\u1019\u103c\u1004\u103a\u1016\u1030\u1038\u101e\u1031\u102c \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1021\u101e\u1005\u103a\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u1021\u101e\u102f\u1036\u1038\u1001\u103b\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u100a\u1036\u1037\u1016\u103b\u1004\u103a\u1038\u1005\u103d\u102c \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1016\u103d\u101a\u103a\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1015\u103c\u103f\u1014\u102c\u1000\u102d\u102f \u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101b\u1014\u103a \u1021\u1005\u102c\u1038 <strong>lasso regression<\/strong> \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u1031\u102c \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>RSS + \u03bb\u03a3|\u03b2 <sub>j<\/sub> |<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>j<\/em> \u101e\u100a\u103a 1 \u1019\u103e <em>p<\/em> \u1014\u103e\u1004\u1037\u103a \u03bb \u2265 0 \u101b\u103e\u102d\u101b\u102c\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u1024\u1012\u102f\u1010\u102d\u101a\u1021\u1001\u1031\u102b\u103a\u1021\u101d\u1031\u102b\u103a\u1000\u102d\u102f <em>\u101b\u102f\u1015\u103a\u101e\u102d\u1019\u103a\u1038\u1015\u103c\u1005\u103a\u1012\u100f\u103a<\/em> \u101f\u102f \u1001\u1031\u102b\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb = 0 \u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1024\u1015\u103c\u1005\u103a\u1012\u100f\u103a\u1021\u101e\u102f\u1036\u1038\u1021\u1014\u103e\u102f\u1014\u103a\u1038\u101e\u100a\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u1015\u102b\u104a lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1021\u1016\u103c\u1005\u103a\u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u03bb \u1021\u1014\u1014\u1039\u1010\u101e\u102d\u102f\u1037 \u1001\u103b\u1009\u103a\u1038\u1000\u1015\u103a\u101c\u102c\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u1021\u1019\u103b\u103e\u104a \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1001\u103c\u1004\u103a\u1038\u1015\u103c\u1005\u103a\u1012\u100f\u103a\u101e\u100a\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u101e\u103c\u1007\u102c\u1000\u103c\u102e\u1038\u1019\u102c\u1038\u101c\u102c\u1015\u103c\u102e\u1038 \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u102d\u102f\u1037 \u1010\u1004\u103a\u101e\u103d\u1004\u103a\u1038\u104d\u1019\u101b\u101e\u1031\u102c \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101e\u102f\u100a\u1021\u1011\u102d \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101c\u102d\u102f\u1000\u103a\u1015\u103c\u102e\u1038 \u1021\u1001\u103b\u102d\u102f\u1037\u1000\u102d\u102f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103e\u1015\u1004\u103a \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u101c\u102d\u102f\u1000\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Lasso regression \u1000\u102d\u102f \u1018\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u101e\u102f\u1036\u1038\u1010\u102c\u101c\u1032\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038 \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1019\u103b\u102c\u1038 \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1001\u103c\u1004\u103a\u1038\u1011\u1000\u103a lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1001\u103c\u1004\u103a\u1038\u104f \u1021\u102c\u1038\u101e\u102c\u1001\u103b\u1000\u103a\u1019\u103e\u102c <a href=\"https:\/\/statorials.org\/my\/\u1018\u1000\u103a\u101c\u102d\u102f\u1000\u103a\u1019\u103e\u102f\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f-\u1021\u1015\u1031\u1038\u1021\u101a\u1030\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1018\u1000\u103a\u101c\u102d\u102f\u1000\u103a-\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f \u1016\u101c\u103e\u101a\u103a\u1019\u103e\u102f<\/a> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mean Square Error (MSE) \u101e\u100a\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u1005\u103a\u1001\u102f\u104f \u1010\u102d\u1000\u103b\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a \u1019\u1000\u103a\u1011\u101b\u1005\u103a\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1011\u102c\u1038\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE = Var( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> )) + [Bias( <em class=\"ph i\">f\u0302(<\/em> x <sub>0<\/sub> ))] <sup>2<\/sup> + Var(\u03b5)<\/span><\/p>\n<p> <span style=\"color: #000000;\">MSE = Variance + Bias <sup>2<\/sup> + Irreducible \u1021\u1019\u103e\u102c\u1038<\/span><\/p>\n<p> <span style=\"color: #000000;\">lasso regression \u104f \u1021\u1001\u103c\u1031\u1001\u1036\u1021\u101a\u1030\u1021\u1006\u1019\u103e\u102c \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1005\u103d\u102c \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 MSE \u1010\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u1014\u102d\u1019\u1037\u103a\u1000\u103b\u1005\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u101e\u1031\u102c\u1018\u1000\u103a\u101c\u102d\u102f\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u102d\u1010\u103a\u1006\u1000\u103a\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101a\u1004\u103a\u1038\u1000\u102d\u102f \u101e\u101b\u102f\u1015\u103a\u1016\u1031\u102c\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1002\u101b\u1015\u103a\u1000\u102d\u102f \u101e\u102f\u1036\u1038\u101e\u1015\u103a\u1015\u102b\u104b<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11851 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/crete1.png\" alt=\"Ridge Regression Bias-Variance Tradeoff\" width=\"468\" height=\"341\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u03bb \u1010\u102d\u102f\u1038\u101c\u102c\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u1021\u1019\u103b\u103e \u1018\u1000\u103a\u101c\u102d\u102f\u1000\u103a\u1019\u103e\u102f \u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a\u1010\u102d\u102f\u1038\u101c\u102c\u101e\u1016\u103c\u1004\u1037\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u101c\u103b\u1031\u102c\u1037\u1000\u103b\u101e\u103d\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104b \u101e\u102d\u102f\u1037\u101b\u102c\u1010\u103d\u1004\u103a\u104a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1021\u1001\u103b\u1000\u103a\u1000\u102d\u102f\u1000\u103b\u1031\u102c\u103a\u101c\u103d\u1014\u103a\u1015\u102b\u1000\u104a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a \u101c\u103b\u1004\u103a\u1019\u103c\u1014\u103a\u1005\u103d\u102c\u101c\u103b\u1031\u102c\u1037\u1014\u100a\u103a\u1038\u101e\u103d\u102c\u1038\u1015\u103c\u102e\u1038 \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038 \u1000\u103b\u1006\u1004\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u101c\u103b\u103e\u1031\u102c\u1037\u1010\u103d\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1006\u102e\u101e\u102d\u102f\u1037 \u1026\u1038\u1010\u100a\u103a\u1005\u1031\u1015\u103c\u102e\u1038 \u1018\u1000\u103a\u101c\u102d\u102f\u1000\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u1010\u102d\u102f\u1038\u101c\u102c\u1005\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1018\u1000\u103a\u101c\u102d\u102f\u1000\u103a\u1019\u103e\u102f \u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1000\u103c\u102c\u1038 \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1006\u102f\u1036\u1038\u101e\u1031\u102c \u1021\u1015\u1031\u1038\u1021\u101a\u1030\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u1037\u103a \u03bb \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u101e\u1031\u102c\u1021\u1001\u102b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f MSE \u101e\u100a\u103a \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1002\u101b\u1015\u103a\u1019\u103e \u1019\u103c\u1004\u103a\u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb = 0 \u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1021\u1001\u102b\u104a lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1015\u103c\u1005\u103a\u1012\u100f\u103a\u1021\u101e\u102f\u1036\u1038\u1021\u1014\u103e\u102f\u1014\u103a\u1038\u101e\u100a\u103a \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1021\u1016\u103c\u1005\u103a\u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1021\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u03bb \u1000\u102d\u102f\u1010\u102d\u102f\u1038\u1019\u103c\u103e\u1004\u1037\u103a\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f MSE \u1010\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11874 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/lasso1.png\" alt=\"Lasso Regression Bias-Variance Tradeoff\" width=\"490\" height=\"357\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c lasso regression \u1016\u103c\u1004\u1037\u103a \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u101e\u1031\u102c model \u101e\u100a\u103a \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038 squares regression \u1016\u103c\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101e\u1031\u102c model \u1011\u1000\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u101e\u1031\u102c test error \u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101c\u102d\u1019\u1037\u103a\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f vs Ridge \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Lasso regression \u1014\u103e\u1004\u1037\u103a <a href=\"https:\/\/statorials.org\/my\/\u1010\u1031\u102c\u1004\u103a\u1000\u103c\u1031\u102c\u104f\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">Ridge regression \u1010\u102d\u102f\u1037\u1000\u102d\u102f<\/a> <em>\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038<\/em> \u1021\u1016\u103c\u1005\u103a \u101c\u1030\u101e\u102d\u1019\u103b\u102c\u1038\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1014\u103e\u1005\u103a\u1026\u1038\u1005\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1019\u103b\u102c\u1038 (RSS) \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1015\u103c\u1005\u103a\u1012\u100f\u103a\u101e\u1000\u103a\u1010\u1019\u103a\u1038\u1000\u102d\u102f \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101b\u1014\u103a \u1000\u103c\u102d\u102f\u1038\u1015\u1019\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1010\u1005\u103a\u1014\u100a\u103a\u1038\u1006\u102d\u102f\u101b\u101e\u1031\u102c\u103a\u104a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u104f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u1014\u1037\u103a\u101e\u1010\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a <em>\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1001\u103c\u1004\u103a\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a<\/em> \u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101b\u102c\u1010\u103d\u1004\u103a\u104a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c \u1015\u103c\u1005\u103a\u1012\u100f\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1019\u103e\u102c \u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101e\u100a\u103a <strong>RSS + \u03bb\u03a3|\u03b2 <sub>j<\/sub> | \u1000\u102d\u102f<\/strong> \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101b\u1014\u103a \u1000\u103c\u102d\u102f\u1038\u1015\u1019\u103a\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ridge regression \u101e\u100a\u103a <strong>RSS + \u03bb\u03a3\u03b2 <sub>j<\/sub> <sup>2<\/sup> \u1000\u102d\u102f<\/strong> \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101b\u1014\u103a \u1000\u103c\u102d\u102f\u1038\u1015\u1019\u103a\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1001\u1031\u102b\u1004\u103a\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1010\u102d\u102f\u1004\u103a\u1038\u104f \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101e\u102f\u100a\u101e\u102d\u102f\u1037 \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1021\u1014\u1000\u103a\u1019\u103e <em>\u101e\u102f\u100a\u101e\u102d\u102f\u1037 \u101c\u102f\u1036\u1038\u101c\u102f\u1036\u1038\u101c\u103b\u102c\u1038\u101c\u103b\u102c\u1038<\/em> \u1019\u101e\u103d\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1015\u103c\u1014\u103a\u1021\u101c\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a lasso regression \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c coefficients \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u03bb \u101c\u102f\u1036\u101c\u1031\u102c\u1000\u103a\u1005\u103d\u102c\u1000\u103c\u102e\u1038\u101c\u102c\u101e\u1031\u102c\u1021\u1001\u102b <em>\u101c\u102f\u1036\u1038\u101d\u101e\u102f\u100a<\/em> \u1016\u103c\u1005\u103a\u101e\u103d\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1015\u102d\u102f\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c\u1021\u101b\u104a lasso regression \u101e\u100a\u103a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038 \u1021\u1005\u102f\u1001\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u101e\u102c\u1015\u102b\u101d\u1004\u103a\u101e\u100a\u1037\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u1037\u103a &#8220; sparse&#8221;  \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u101c\u102f\u1015\u103a\u1014\u102d\u102f\u1004\u103a\u1005\u103d\u1019\u103a\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u100a\u103a\u1019\u103e\u102c \u1019\u1031\u1038\u1005\u101b\u102c\u1016\u103c\u1005\u103a\u101c\u102c\u101e\u100a\u103a- <strong>\u1010\u1031\u102c\u1004\u103a\u1000\u103c\u1031\u102c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u101c\u1000\u103a\u1005\u1010\u102d\u102f\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1015\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u101e\u101c\u102c\u1038\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1016\u103c\u1031- \u1021\u1032\u1012\u102b\u1019\u1030\u1010\u100a\u103a\u1010\u101a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a\u101e\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u100a\u1037\u103a\u1000\u102d\u1005\u1039\u1005\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a\u104a lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103e\u102c \u1021\u101b\u1031\u1038\u1019\u1015\u102b\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101e\u102f\u100a\u1021\u1011\u102d \u101c\u102f\u1036\u1038\u101c\u102f\u1036\u1038\u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103e\u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1015\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u103d\u1004\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u101e\u100a\u103a \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f coefficients \u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1001\u1031\u102b\u1004\u103a\u1006\u102f\u1010\u103a\u1006\u102f\u1010\u103a\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u103d\u1004\u103a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u1011\u102d\u1014\u103a\u1038\u101e\u102d\u1019\u103a\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1015\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101b\u102c\u1010\u103d\u1004\u103a \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000 \u1021\u1011\u102d\u101b\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/k-cross-validation-\u1000\u102d\u102f-\u1001\u1031\u102b\u1000\u103a\u1015\u102b\u104b\/\" target=\"_blank\" rel=\"noopener noreferrer\">k-fold cross-validation \u1000\u102d\u102f<\/a> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u1006\u102d\u102f \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038 mean square error (MSE) \u1000\u102d\u102f \u1011\u102f\u1010\u103a\u1015\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038 \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a lasso regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">lasso regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1- \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1006\u1000\u103a\u1005\u1015\u103a\u1019\u1000\u103a\u1011\u101b\u1005\u103a\u1014\u103e\u1004\u1037\u103a VIF \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u1000\u103a\u1011\u101b\u1005\u103a\u1000\u102d\u102f-\u1018\u101a\u103a\u101c\u102d\u102f\u1016\u1010\u103a\u1019\u101c\u1032\u104b\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u1000\u103a\u1011\u101b\u1005\u103a<\/a> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u101c\u102f\u1015\u103a\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a <a href=\"https:\/\/statorials.org\/my\/multicollinearity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">VIF (variance inflation factor) \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/a> \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c VIF \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1001\u102d\u102f\u1004\u103a\u1019\u102c\u101e\u1031\u102c\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1015\u102b\u1000 (\u1021\u1001\u103b\u102d\u102f\u1037\u1005\u102c\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a &#8220; \u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c&#8221;  VIF \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f 5 \u1021\u1016\u103c\u1005\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1021\u1001\u103b\u102d\u102f\u1037\u1000 10 \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a)\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1012\u1031\u1010\u102c\u1010\u103d\u1004\u103a multicollinearity \u1019\u101b\u103e\u102d\u1015\u102b\u1000\u104a \u1015\u1011\u1019\u1014\u1031\u101b\u102c\u1010\u103d\u1004\u103a lasso regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1019\u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u104b \u101a\u1004\u103a\u1038\u1021\u1005\u102c\u1038\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101e\u102c\u1019\u1014\u103a\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038 \u101c\u1031\u1038\u1011\u1031\u102c\u1004\u1037\u103a\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u103c\u102e\u1038 \u03bb \u1021\u1010\u103d\u1000\u103a \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">lasso regression \u101e\u100a\u103a \u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u1015\u103c\u102e\u1038\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u03bb \u1021\u1010\u103d\u1000\u103a \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d (\u101c\u1030\u1000\u103c\u102d\u102f\u1000\u103a\u1019\u103b\u102c\u1038\u101e\u1031\u102c \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1038\u1019\u1004\u103a\u1038\u1018\u102c\u101e\u102c\u1005\u1000\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u1032\u1037\u101e\u102d\u102f\u1037 R \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a Python \u1000\u1032\u1037\u101e\u102d\u102f\u1037) \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u101c\u102f\u1015\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bb \u1021\u1010\u103d\u1000\u103a \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u03bb \u1021\u1010\u103d\u1000\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1000\u102c \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1000\u102d\u102f \u1016\u103c\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038 MSE \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u1037\u103a \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1021\u1016\u103c\u1005\u103a \u03bb \u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u102c\u1038 \u1001\u1031\u102b\u1004\u103a\u1006\u102f\u1010\u103a\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a \u101e\u102c\u1019\u1014\u103a\u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f k-fold cross-validation \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000 \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038 MSE \u1000\u102d\u102f\u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1001\u1031\u102b\u1004\u103a\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u102c\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1004\u1037\u103a \u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u102d\u102f\u1037\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1021\u1015\u1031\u102b\u103a\u1019\u1030\u1010\u100a\u103a\u104d \u1024\u1015\u102f\u1036\u1005\u1036\u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038\u1011\u1032\u1019\u103e \u1010\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u1011\u1000\u103a \u1005\u103d\u1019\u103a\u1038\u1006\u1031\u102c\u1004\u103a\u101b\u100a\u103a\u1015\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u101c\u102c\u1019\u100a\u103a\u1019\u103e\u102c \u101c\u102f\u1036\u1038\u101d\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>R &amp; Python \u1010\u103d\u1004\u103a Lasso Regression<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a R \u1014\u103e\u1004\u1037\u103a Python \u1010\u103d\u1004\u103a lasso regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102f\u1036\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a \u104b<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-lasso-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">R in Lasso Regression (\u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a)<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/python-\u1010\u103d\u1004\u103a-lasso-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">Python \u101b\u103e\u102d Lasso \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f (\u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u101e\u102c\u1019\u102c\u1014\u103a \u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1019\u103b\u102d\u102f\u1038\u1005\u102f\u1036\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u104f\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a p \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a- Y = \u03b2 0 + \u03b2 1 X 1 + \u03b2 2 X 2 + \u2026 + \u03b2 p \u101b\u103d\u103e\u1031- Y : \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a X j : j th \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u03b2 j : X j \u1010\u103d\u1004\u103a \u1010\u1005\u103a\u101a\u1030\u1014\u1005\u103a\u1010\u102d\u102f\u1038\u101c\u102c\u1019\u103e\u102f\u104f Y \u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1001\u103c\u102c\u1038\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u101e\u1031\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u100a\u103a \u03b5 : [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Lasso Regression \u1014\u102d\u1012\u102b\u1014\u103a\u1038 - Statology<\/title>\n<meta name=\"description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1021\u1015\u102b\u1021\u101d\u1004\u103a lasso regression \u1000\u102d\u102f \u1014\u102d\u1012\u102b\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1015\u1031\u1038\u1015\u102b\u101e\u100a\u103a\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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