2272:
3206:
2495:
2836:
3099:
2135:
2956:
2346:
1305:
estimate can be significantly affected. Avoiding this requires reducing the frequency of collision counter updates between any two distinct elements. This is achieved by replacing each
3387:
2626:
3029:
1790:
2698:
1685:
1639:
1505:
1259:
3498:
986:
algorithm by John Moody, but differs in its use of hash functions with low dependence, which makes it more practical. In order to still have a high probability of success, the
3298:
3252:
1117:
1960:
1917:
3593:
Faisal M. Algashaam; Kien Nguyen; Mohamed
Alkanhal; Vinod Chandran; Wageeh Boles. "Multispectral Periocular Classification WithMultimodal Compact Multi-Linear Pooling" .
2743:
3648:
Alon, Noga, Yossi Matias, and Mario
Szegedy. "The space complexity of approximating the frequency moments." Journal of Computer and system sciences 58.1 (1999): 137-147.
1736:
3841:
Faisal M. Algashaam; Kien Nguyen; Mohamed
Alkanhal; Vinod Chandran; Wageeh Boles. "Multispectral Periocular Classification WithMultimodal Compact Multi-Linear Pooling"
2554:
3675:
Larsen, Kasper Green, Rasmus Pagh, and Jakub Tětek. "CountSketches, Feature
Hashing and the Median of Three." International Conference on Machine Learning. PMLR, 2021.
3542:
2042:
3453:
3420:
1367:
2871:
1593:
866:
2991:
2656:
2522:
2396:
1874:
1844:
1817:
1398:
1330:
1178:
1151:
1303:
1062:
904:
2006:
3518:
3119:
2366:
2158:
1980:
1558:
1538:
861:
851:
2166:
692:
899:
972:
856:
707:
438:
939:
742:
3124:
2401:
818:
3892:
367:
2756:
876:
639:
174:
3034:
3887:
3666:
Woodruff, David P. "Sketching as a Tool for
Numerical Linear Algebra." Theoretical Computer Science 10.1-2 (2014): 1–157.
2050:
894:
979:
of streams (these calculations require counting of the number of occurrences for the distinct elements of the stream).
727:
702:
651:
3657:
Moody, John. "Fast learning in multi-resolution hierarchies." Advances in neural information processing systems. 1989.
3556:
775:
770:
423:
2879:
433:
71:
2280:
3693:. SIGKDD international conference on Knowledge discovery and data mining. Association for Computing Machinery.
3327:
932:
828:
592:
413:
2559:
1268:
the previous construct still has a major deficiency: if a lower-frequency-but-still-important output element
803:
505:
281:
3882:
2999:
760:
697:
607:
585:
428:
418:
2753:
Alternatively Count-Sketch can be seen as a linear mapping with a non-linear reconstruction function. Let
1741:
911:
823:
808:
269:
91:
2661:
1644:
1598:
1411:
1187:
3571:
is a version of algorithm with smaller memory requirements (and weaker error guarantees as a tradeoff).
3461:
871:
798:
548:
443:
231:
164:
124:
971:. It was invented by Moses Charikar, Kevin Chen and Martin Farach-Colton in an effort to speed up the
3257:
3211:
925:
531:
299:
169:
1074:
956:
553:
473:
396:
314:
144:
106:
101:
61:
56:
1922:
1879:
2703:
1373:
of a particular counter to be incremented/decremented selected via another set of hash functions
1013:
The inventors of this data structure offer the following iterative explanation of its operation:
998:
500:
349:
249:
76:
3807:
1690:
3552:
2527:
680:
656:
558:
319:
294:
254:
66:
3527:
2011:
3425:
3392:
1339:
634:
456:
408:
264:
179:
51:
3740:"Analytical model of the digital antenna array on a basis of face-splitting matrix products"
2841:
1563:
3568:
2964:
2634:
2500:
2374:
1852:
1822:
1795:
1376:
1308:
1156:
1129:
563:
513:
1279:
1038:
8:
666:
602:
573:
478:
304:
237:
223:
209:
184:
134:
86:
46:
1988:
3784:
3503:
3104:
2351:
2143:
1965:
1543:
1523:
644:
568:
354:
149:
3826:
3853:
3830:
3788:
3608:
3545:
976:
737:
580:
493:
289:
259:
204:
199:
154:
96:
3822:
3776:
3694:
964:
765:
518:
468:
378:
362:
332:
194:
189:
139:
129:
27:
1029:
983:
793:
597:
463:
403:
3842:
1273:
1069:
1002:
994:
813:
344:
81:
2267:{\displaystyle r_{q}={\text{median}}_{i=1}^{d}\,s_{i}(q)\cdot C_{i,h_{i}(q)}.}
3876:
3834:
3769:
Cybernetics and
Systems Analysis C/C of Kibernetika I Sistemnyi Analiz.- 1999
3521:
3309:
1018:
732:
661:
543:
274:
159:
3698:
3858:
3713:
3613:
3574:
987:
3686:
3320:
3313:
538:
32:
1126:
of the previous estimate is to use an array of different hash functions
3780:
3632:
3630:
968:
960:
687:
383:
309:
3739:
846:
627:
3627:
990:
is used to aggregate multiple count sketches, rather than the mean.
3559:
such structures can be computed much faster than normal matrices.
3555:
can be used to do fast convolution of count sketches. By using the
1123:
3761:
1005:
and is a cornerstone in many numerical linear algebra algorithms.
622:
3201:{\displaystyle v_{j}^{*}={\text{median}}_{i}C_{j}^{(i)}s_{i}(j)}
2490:{\displaystyle O(\mathrm {min} \{m_{1}^{2}/w^{2},m_{2}^{2}/w\})}
1336:
counters (making the counter set into a two-dimensional matrix
373:
3691:
Fast and scalable polynomial kernels via explicit feature maps
3208:. This gives the same guarantees as stated above, if we take
617:
612:
339:
3806:
Charikar, Moses; Chen, Kevin; Farach-Colton, Martin (2004).
3762:"A Family of Face Products of Matrices and its Properties"
3805:
3636:
905:
List of datasets in computer vision and image processing
1068:
can be approximated, although extremely poorly, by the
3530:
3506:
3464:
3428:
3395:
3330:
3260:
3214:
3127:
3107:
3037:
3002:
2967:
2882:
2844:
2831:{\displaystyle M^{(i\in )}\in \{-1,0,1\}^{w\times n}}
2759:
2706:
2664:
2637:
2562:
2530:
2503:
2404:
2377:
2354:
2283:
2169:
2146:
2053:
2014:
1991:
1968:
1925:
1882:
1855:
1825:
1798:
1744:
1693:
1647:
1601:
1566:
1546:
1526:
1414:
1379:
1342:
1311:
1282:
1190:
1159:
1132:
1077:
1041:
3094:{\displaystyle C^{(i)}=M^{(i)}v\in \mathbb {R} ^{w}}
1792:. It is necessary that the hash families from which
2130:{\displaystyle C_{i,j}=\sum _{h_{i}(k)=j}s_{i}(k).}
1035:. After a single pass over the data, the frequency
3536:
3512:
3492:
3447:
3414:
3381:
3292:
3246:
3200:
3113:
3093:
3023:
2985:
2950:
2865:
2830:
2737:
2692:
2650:
2620:
2548:
2516:
2489:
2390:
2360:
2340:
2266:
2152:
2129:
2036:
2000:
1974:
1954:
1911:
1868:
1838:
1811:
1784:
1730:
1679:
1633:
1587:
1552:
1532:
1499:
1392:
1361:
1324:
1297:
1253:
1172:
1145:
1111:
1056:
975:by Alon, Matias and Szegedy for approximating the
3874:
3714:"End products in matrices in radar applications"
1017:at the simplest level, the output of a single
900:List of datasets for machine-learning research
2951:{\displaystyle M_{h_{i}(j),j}^{(i)}=s_{i}(j)}
933:
3303:
3281:
3274:
3235:
3228:
2813:
2791:
2481:
2422:
2341:{\displaystyle s_{i}(q)\cdot C_{i,h_{i}(q)}}
1779:
1770:
3852:Ahle, Thomas; Knudsen, Jakob (2019-09-03).
3851:
3721:Radioelectronics and Communications Systems
3607:Ahle, Thomas; Knudsen, Jakob (2019-09-03).
3606:
1560:(to be defined later) independently choose
1332:in the previous construct with an array of
2700:off from the true value, with probability
1515:
940:
926:
3382:{\displaystyle C^{(1)}x\ast C^{(2)}x^{T}}
3081:
3011:
2348:are unbiased estimates of how many times
2206:
3808:"Finding frequent items in data streams"
3684:
2621:{\displaystyle \sum _{q}(\sum _{i})^{2}}
1008:
993:These properties allow use for explicit
3759:
3737:
3711:
3660:
3637:Charikar, Chen & Farach-Colton 2004
3455:are independent count sketch matrices.
3875:
982:The sketch is nearly identical to the
3458:Pham and Pagh show that this equals
3024:{\displaystyle v\in \mathbb {R} ^{n}}
2748:
1265:range will tighten the approximation;
1261:still holds, so averaging across the
1122:a straightforward way to improve the
3312:of two vectors is equivalent to the
2658:is guaranteed to never be more than
2160:s one computes the following value:
1985:At the end of this process, one has
1846:are chosen be pairwise independent.
1153:, each connected to its own counter
3678:
3319:The count sketch computes a vector
3308:The count sketch projection of the
1785:{\displaystyle s_{i}:\to \{\pm 1\}}
895:Glossary of artificial intelligence
13:
3799:
3316:of two component count sketches.
2693:{\displaystyle 2m_{2}/{\sqrt {w}}}
2418:
2415:
2412:
1680:{\displaystyle s_{1},\dots ,s_{d}}
1634:{\displaystyle h_{1},\dots ,h_{d}}
1500:{\displaystyle {\mathbf {E}}=n(q)}
1254:{\displaystyle {\mathbf {E}}=n(q)}
1028:into {+1, -1} is feeding a single
959:that is particularly efficient in
14:
3904:
3760:Slyusar, V. I. (March 13, 1998).
3493:{\displaystyle C(x\otimes x^{T})}
1507:, averaging across all values of
2524:is the length of the stream and
1417:
1193:
1080:
3753:
3731:
3293:{\displaystyle m_{2}=\|v\|_{2}}
3247:{\displaystyle m_{1}=\|v\|_{1}}
1276:with a high-frequency element,
16:Method of a dimension reduction
3854:"Almost Optimal Tensor Sketch"
3705:
3669:
3651:
3642:
3609:"Almost Optimal Tensor Sketch"
3600:
3587:
3487:
3468:
3440:
3434:
3407:
3401:
3364:
3358:
3342:
3336:
3195:
3189:
3174:
3168:
3068:
3062:
3049:
3043:
2980:
2974:
2945:
2939:
2921:
2915:
2904:
2898:
2783:
2780:
2774:
2765:
2730:
2724:
2609:
2605:
2586:
2573:
2484:
2408:
2333:
2327:
2300:
2294:
2256:
2250:
2223:
2217:
2121:
2115:
2094:
2088:
2031:
2015:
1949:
1936:
1906:
1893:
1767:
1764:
1758:
1725:
1719:
1716:
1713:
1707:
1494:
1488:
1479:
1476:
1470:
1452:
1446:
1422:
1292:
1286:
1248:
1242:
1233:
1230:
1224:
1198:
1106:
1103:
1097:
1085:
1051:
1045:
315:Relevance vector machine (RVM)
1:
3893:Probabilistic data structures
3827:10.1016/s0304-3975(03)00400-6
3738:Slyusar, V. I. (1997-05-20).
3580:
1112:{\displaystyle {\mathbf {E}}}
804:Computational learning theory
368:Expectation–maximization (EM)
3815:Theoretical Computer Science
2368:has appeared in the stream.
1955:{\displaystyle h_{j}(q_{i})}
1912:{\displaystyle s_{j}(q_{i})}
761:Coefficient of determination
608:Convolutional neural network
320:Support vector machine (SVM)
7:
3562:
2738:{\displaystyle 1-e^{-O(t)}}
912:Outline of machine learning
809:Empirical risk minimization
10:
3909:
3888:Hash-based data structures
1731:{\displaystyle h_{i}:\to }
549:Feedforward neural network
300:Artificial neural networks
3304:Relation to Tensor sketch
2549:{\displaystyle m_{2}^{2}}
2140:To estimate the count of
532:Artificial neural network
3821:(1). Elsevier BV: 3–15.
3537:{\displaystyle \otimes }
2037:{\displaystyle (C_{ij})}
1024:mapping stream elements
957:dimensionality reduction
841:Journals and conferences
788:Mathematical foundations
698:Temporal difference (TD)
554:Recurrent neural network
474:Conditional random field
397:Dimensionality reduction
145:Dimensionality reduction
107:Quantum machine learning
102:Neuromorphic engineering
62:Self-supervised learning
57:Semi-supervised learning
3712:Slyusar, V. I. (1998).
3699:10.1145/2487575.2487591
3448:{\displaystyle C^{(2)}}
3415:{\displaystyle C^{(1)}}
2993:and 0 everywhere else.
1516:Mathematical definition
1362:{\displaystyle C_{i,j}}
250:Apprenticeship learning
3557:face-splitting product
3553:fast Fourier transform
3538:
3514:
3494:
3449:
3416:
3383:
3294:
3248:
3202:
3115:
3095:
3025:
2987:
2952:
2867:
2866:{\displaystyle d=2t+1}
2832:
2739:
2694:
2652:
2622:
2550:
2518:
2491:
2392:
2362:
2342:
2268:
2154:
2131:
2038:
2002:
1976:
1956:
1913:
1870:
1840:
1813:
1786:
1732:
1681:
1635:
1595:random hash functions
1589:
1588:{\displaystyle d=2t+1}
1554:
1534:
1501:
1394:
1363:
1326:
1299:
1255:
1174:
1147:
1113:
1058:
799:Bias–variance tradeoff
681:Reinforcement learning
657:Spiking neural network
67:Reinforcement learning
3539:
3515:
3495:
3450:
3417:
3384:
3295:
3249:
3203:
3116:
3096:
3026:
2988:
2986:{\displaystyle j\in }
2953:
2873:matrices, defined by
2868:
2838:, be a collection of
2833:
2740:
2695:
2653:
2651:{\displaystyle r_{q}}
2623:
2551:
2519:
2517:{\displaystyle m_{1}}
2492:
2393:
2391:{\displaystyle r_{q}}
2363:
2343:
2269:
2155:
2132:
2039:
2003:
1977:
1957:
1914:
1871:
1869:{\displaystyle q_{i}}
1841:
1839:{\displaystyle s_{i}}
1814:
1812:{\displaystyle h_{i}}
1787:
1733:
1682:
1636:
1590:
1555:
1535:
1502:
1395:
1393:{\displaystyle h_{i}}
1364:
1327:
1325:{\displaystyle C_{i}}
1300:
1256:
1175:
1173:{\displaystyle C_{i}}
1148:
1146:{\displaystyle s_{i}}
1114:
1059:
1009:Intuitive explanation
635:Neural radiance field
457:Structured prediction
180:Structured prediction
52:Unsupervised learning
3747:Proc. ICATT-97, Kyiv
3528:
3504:
3462:
3426:
3393:
3328:
3258:
3212:
3125:
3105:
3035:
3000:
2965:
2880:
2842:
2757:
2704:
2662:
2635:
2560:
2528:
2501:
2402:
2375:
2352:
2281:
2167:
2144:
2051:
2012:
1989:
1966:
1923:
1880:
1853:
1823:
1796:
1742:
1691:
1645:
1599:
1564:
1544:
1524:
1412:
1377:
1340:
1309:
1298:{\displaystyle n(a)}
1280:
1188:
1157:
1130:
1075:
1064:of a stream element
1057:{\displaystyle n(q)}
1039:
824:Statistical learning
722:Learning with humans
514:Local outlier factor
3883:Dimension reduction
3178:
3142:
2925:
2545:
2472:
2439:
2205:
1876:in the stream, add
1404:into the range {1..
1180:. For each element
667:Electrochemical RAM
574:reservoir computing
305:Logistic regression
224:Supervised learning
210:Multimodal learning
185:Feature engineering
130:Generative modeling
92:Rule-based learning
87:Curriculum learning
47:Supervised learning
22:Part of a series on
3781:10.1007/BF02733426
3534:
3524:of vectors, where
3510:
3490:
3445:
3412:
3379:
3290:
3244:
3198:
3158:
3128:
3111:
3091:
3021:
2983:
2948:
2883:
2863:
2828:
2749:Vector formulation
2735:
2690:
2648:
2618:
2585:
2572:
2546:
2531:
2514:
2487:
2458:
2425:
2388:
2358:
2338:
2264:
2183:
2150:
2127:
2104:
2034:
2001:{\displaystyle wd}
1998:
1972:
1952:
1909:
1866:
1836:
1809:
1782:
1728:
1677:
1631:
1585:
1550:
1530:
1497:
1390:
1359:
1322:
1295:
1251:
1170:
1143:
1109:
1054:
235: •
150:Density estimation
3546:Kronecker product
3513:{\displaystyle C}
3500:– a count sketch
3150:
3114:{\displaystyle v}
3101:. To reconstruct
2688:
2576:
2563:
2361:{\displaystyle q}
2187:
2153:{\displaystyle q}
2073:
1975:{\displaystyle j}
1962:th bucket of the
1849:2. For each item
1553:{\displaystyle t}
1533:{\displaystyle w}
1520:1. For constants
1400:that map element
977:frequency moments
950:
949:
755:Model diagnostics
738:Human-in-the-loop
581:Boltzmann machine
494:Anomaly detection
290:Linear regression
205:Ontology learning
200:Grammar induction
175:Semantic analysis
170:Association rules
155:Anomaly detection
97:Neuro-symbolic AI
3900:
3869:
3867:
3866:
3838:
3812:
3793:
3792:
3766:
3757:
3751:
3750:
3744:
3735:
3729:
3728:
3718:
3709:
3703:
3702:
3682:
3676:
3673:
3667:
3664:
3658:
3655:
3649:
3646:
3640:
3634:
3625:
3624:
3622:
3621:
3604:
3598:
3591:
3569:Count–min sketch
3543:
3541:
3540:
3535:
3519:
3517:
3516:
3511:
3499:
3497:
3496:
3491:
3486:
3485:
3454:
3452:
3451:
3446:
3444:
3443:
3421:
3419:
3418:
3413:
3411:
3410:
3388:
3386:
3385:
3380:
3378:
3377:
3368:
3367:
3346:
3345:
3299:
3297:
3296:
3291:
3289:
3288:
3270:
3269:
3253:
3251:
3250:
3245:
3243:
3242:
3224:
3223:
3207:
3205:
3204:
3199:
3188:
3187:
3177:
3166:
3157:
3156:
3151:
3148:
3141:
3136:
3120:
3118:
3117:
3112:
3100:
3098:
3097:
3092:
3090:
3089:
3084:
3072:
3071:
3053:
3052:
3030:
3028:
3027:
3022:
3020:
3019:
3014:
2992:
2990:
2989:
2984:
2957:
2955:
2954:
2949:
2938:
2937:
2924:
2913:
2897:
2896:
2872:
2870:
2869:
2864:
2837:
2835:
2834:
2829:
2827:
2826:
2787:
2786:
2744:
2742:
2741:
2736:
2734:
2733:
2699:
2697:
2696:
2691:
2689:
2684:
2682:
2677:
2676:
2657:
2655:
2654:
2649:
2647:
2646:
2627:
2625:
2624:
2619:
2617:
2616:
2598:
2597:
2584:
2571:
2555:
2553:
2552:
2547:
2544:
2539:
2523:
2521:
2520:
2515:
2513:
2512:
2496:
2494:
2493:
2488:
2477:
2471:
2466:
2454:
2453:
2444:
2438:
2433:
2421:
2397:
2395:
2394:
2389:
2387:
2386:
2367:
2365:
2364:
2359:
2347:
2345:
2344:
2339:
2337:
2336:
2326:
2325:
2293:
2292:
2273:
2271:
2270:
2265:
2260:
2259:
2249:
2248:
2216:
2215:
2204:
2199:
2188:
2185:
2179:
2178:
2159:
2157:
2156:
2151:
2136:
2134:
2133:
2128:
2114:
2113:
2103:
2087:
2086:
2069:
2068:
2043:
2041:
2040:
2035:
2030:
2029:
2007:
2005:
2004:
1999:
1981:
1979:
1978:
1973:
1961:
1959:
1958:
1953:
1948:
1947:
1935:
1934:
1918:
1916:
1915:
1910:
1905:
1904:
1892:
1891:
1875:
1873:
1872:
1867:
1865:
1864:
1845:
1843:
1842:
1837:
1835:
1834:
1818:
1816:
1815:
1810:
1808:
1807:
1791:
1789:
1788:
1783:
1754:
1753:
1737:
1735:
1734:
1729:
1703:
1702:
1686:
1684:
1683:
1678:
1676:
1675:
1657:
1656:
1640:
1638:
1637:
1632:
1630:
1629:
1611:
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1594:
1592:
1591:
1586:
1559:
1557:
1556:
1551:
1539:
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1531:
1510:
1506:
1504:
1503:
1498:
1469:
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1456:
1455:
1445:
1444:
1421:
1420:
1407:
1403:
1399:
1397:
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1391:
1389:
1388:
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1366:
1365:
1360:
1358:
1357:
1335:
1331:
1329:
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1320:
1304:
1302:
1301:
1296:
1271:
1264:
1260:
1258:
1257:
1252:
1223:
1222:
1210:
1209:
1197:
1196:
1183:
1179:
1177:
1176:
1171:
1169:
1168:
1152:
1150:
1149:
1144:
1142:
1141:
1118:
1116:
1115:
1110:
1084:
1083:
1067:
1063:
1061:
1060:
1055:
1034:
1027:
1023:
965:machine learning
942:
935:
928:
889:Related articles
766:Confusion matrix
519:Isolation forest
464:Graphical models
243:
242:
195:Learning to rank
190:Feature learning
28:Machine learning
19:
18:
3908:
3907:
3903:
3902:
3901:
3899:
3898:
3897:
3873:
3872:
3864:
3862:
3848:, Vol. 5. 2017.
3810:
3802:
3800:Further reading
3797:
3796:
3764:
3758:
3754:
3742:
3736:
3732:
3716:
3710:
3706:
3683:
3679:
3674:
3670:
3665:
3661:
3656:
3652:
3647:
3643:
3635:
3628:
3619:
3617:
3605:
3601:
3597:, Vol. 5. 2017.
3592:
3588:
3583:
3565:
3529:
3526:
3525:
3505:
3502:
3501:
3481:
3477:
3463:
3460:
3459:
3433:
3429:
3427:
3424:
3423:
3400:
3396:
3394:
3391:
3390:
3373:
3369:
3357:
3353:
3335:
3331:
3329:
3326:
3325:
3306:
3284:
3280:
3265:
3261:
3259:
3256:
3255:
3238:
3234:
3219:
3215:
3213:
3210:
3209:
3183:
3179:
3167:
3162:
3152:
3147:
3146:
3137:
3132:
3126:
3123:
3122:
3106:
3103:
3102:
3085:
3080:
3079:
3061:
3057:
3042:
3038:
3036:
3033:
3032:
3031:is sketched by
3015:
3010:
3009:
3001:
2998:
2997:
2966:
2963:
2962:
2933:
2929:
2914:
2892:
2888:
2887:
2881:
2878:
2877:
2843:
2840:
2839:
2816:
2812:
2764:
2760:
2758:
2755:
2754:
2751:
2717:
2713:
2705:
2702:
2701:
2683:
2678:
2672:
2668:
2663:
2660:
2659:
2642:
2638:
2636:
2633:
2632:
2612:
2608:
2593:
2589:
2580:
2567:
2561:
2558:
2557:
2540:
2535:
2529:
2526:
2525:
2508:
2504:
2502:
2499:
2498:
2473:
2467:
2462:
2449:
2445:
2440:
2434:
2429:
2411:
2403:
2400:
2399:
2382:
2378:
2376:
2373:
2372:
2353:
2350:
2349:
2321:
2317:
2310:
2306:
2288:
2284:
2282:
2279:
2278:
2244:
2240:
2233:
2229:
2211:
2207:
2200:
2189:
2184:
2174:
2170:
2168:
2165:
2164:
2145:
2142:
2141:
2109:
2105:
2082:
2078:
2077:
2058:
2054:
2052:
2049:
2048:
2022:
2018:
2013:
2010:
2009:
1990:
1987:
1986:
1967:
1964:
1963:
1943:
1939:
1930:
1926:
1924:
1921:
1920:
1900:
1896:
1887:
1883:
1881:
1878:
1877:
1860:
1856:
1854:
1851:
1850:
1830:
1826:
1824:
1821:
1820:
1803:
1799:
1797:
1794:
1793:
1749:
1745:
1743:
1740:
1739:
1698:
1694:
1692:
1689:
1688:
1671:
1667:
1652:
1648:
1646:
1643:
1642:
1625:
1621:
1606:
1602:
1600:
1597:
1596:
1565:
1562:
1561:
1545:
1542:
1541:
1525:
1522:
1521:
1518:
1508:
1464:
1460:
1440:
1436:
1429:
1425:
1416:
1415:
1413:
1410:
1409:
1405:
1401:
1384:
1380:
1378:
1375:
1374:
1370:
1347:
1343:
1341:
1338:
1337:
1333:
1316:
1312:
1310:
1307:
1306:
1281:
1278:
1277:
1269:
1262:
1218:
1214:
1205:
1201:
1192:
1191:
1189:
1186:
1185:
1181:
1164:
1160:
1158:
1155:
1154:
1137:
1133:
1131:
1128:
1127:
1079:
1078:
1076:
1073:
1072:
1065:
1040:
1037:
1036:
1032:
1030:up/down counter
1025:
1021:
1011:
1003:neural networks
984:Feature hashing
946:
917:
916:
890:
882:
881:
842:
834:
833:
794:Kernel machines
789:
781:
780:
756:
748:
747:
728:Active learning
723:
715:
714:
683:
673:
672:
598:Diffusion model
534:
524:
523:
496:
486:
485:
459:
449:
448:
404:Factor analysis
399:
389:
388:
372:
335:
325:
324:
245:
244:
228:
227:
226:
215:
214:
120:
112:
111:
77:Online learning
42:
30:
17:
12:
11:
5:
3906:
3896:
3895:
3890:
3885:
3871:
3870:
3849:
3839:
3801:
3798:
3795:
3794:
3775:(3): 379–384.
3752:
3730:
3704:
3677:
3668:
3659:
3650:
3641:
3626:
3599:
3585:
3584:
3582:
3579:
3578:
3577:
3572:
3564:
3561:
3533:
3509:
3489:
3484:
3480:
3476:
3473:
3470:
3467:
3442:
3439:
3436:
3432:
3409:
3406:
3403:
3399:
3376:
3372:
3366:
3363:
3360:
3356:
3352:
3349:
3344:
3341:
3338:
3334:
3305:
3302:
3287:
3283:
3279:
3276:
3273:
3268:
3264:
3241:
3237:
3233:
3230:
3227:
3222:
3218:
3197:
3194:
3191:
3186:
3182:
3176:
3173:
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3165:
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3145:
3140:
3135:
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3110:
3088:
3083:
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3075:
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3067:
3064:
3060:
3056:
3051:
3048:
3045:
3041:
3018:
3013:
3008:
3005:
2996:Then a vector
2982:
2979:
2976:
2973:
2970:
2959:
2958:
2947:
2944:
2941:
2936:
2932:
2928:
2923:
2920:
2917:
2912:
2909:
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2903:
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2862:
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2853:
2850:
2847:
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2808:
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2796:
2793:
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2432:
2428:
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2420:
2417:
2414:
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2381:
2357:
2335:
2332:
2329:
2324:
2320:
2316:
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2309:
2305:
2302:
2299:
2296:
2291:
2287:
2275:
2274:
2263:
2258:
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2252:
2247:
2243:
2239:
2236:
2232:
2228:
2225:
2222:
2219:
2214:
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2198:
2195:
2192:
2182:
2177:
2173:
2149:
2138:
2137:
2126:
2123:
2120:
2117:
2112:
2108:
2102:
2099:
2096:
2093:
2090:
2085:
2081:
2076:
2072:
2067:
2064:
2061:
2057:
2033:
2028:
2025:
2021:
2017:
1997:
1994:
1971:
1951:
1946:
1942:
1938:
1933:
1929:
1908:
1903:
1899:
1895:
1890:
1886:
1863:
1859:
1833:
1829:
1806:
1802:
1781:
1778:
1775:
1772:
1769:
1766:
1763:
1760:
1757:
1752:
1748:
1727:
1724:
1721:
1718:
1715:
1712:
1709:
1706:
1701:
1697:
1674:
1670:
1666:
1663:
1660:
1655:
1651:
1628:
1624:
1620:
1617:
1614:
1609:
1605:
1584:
1581:
1578:
1575:
1572:
1569:
1549:
1529:
1517:
1514:
1513:
1512:
1496:
1493:
1490:
1487:
1484:
1481:
1478:
1475:
1472:
1467:
1463:
1459:
1454:
1451:
1448:
1443:
1439:
1435:
1432:
1428:
1424:
1419:
1387:
1383:
1369:), with index
1356:
1353:
1350:
1346:
1319:
1315:
1294:
1291:
1288:
1285:
1274:hash collision
1266:
1250:
1247:
1244:
1241:
1238:
1235:
1232:
1229:
1226:
1221:
1217:
1213:
1208:
1204:
1200:
1195:
1167:
1163:
1140:
1136:
1120:
1108:
1105:
1102:
1099:
1096:
1093:
1090:
1087:
1082:
1070:expected value
1053:
1050:
1047:
1044:
1010:
1007:
995:kernel methods
948:
947:
945:
944:
937:
930:
922:
919:
918:
915:
914:
909:
908:
907:
897:
891:
888:
887:
884:
883:
880:
879:
874:
869:
864:
859:
854:
849:
843:
840:
839:
836:
835:
832:
831:
826:
821:
816:
814:Occam learning
811:
806:
801:
796:
790:
787:
786:
783:
782:
779:
778:
773:
771:Learning curve
768:
763:
757:
754:
753:
750:
749:
746:
745:
740:
735:
730:
724:
721:
720:
717:
716:
713:
712:
711:
710:
700:
695:
690:
684:
679:
678:
675:
674:
671:
670:
664:
659:
654:
649:
648:
647:
637:
632:
631:
630:
625:
620:
615:
605:
600:
595:
590:
589:
588:
578:
577:
576:
571:
566:
561:
551:
546:
541:
535:
530:
529:
526:
525:
522:
521:
516:
511:
503:
497:
492:
491:
488:
487:
484:
483:
482:
481:
476:
471:
460:
455:
454:
451:
450:
447:
446:
441:
436:
431:
426:
421:
416:
411:
406:
400:
395:
394:
391:
390:
387:
386:
381:
376:
370:
365:
360:
352:
347:
342:
336:
331:
330:
327:
326:
323:
322:
317:
312:
307:
302:
297:
292:
287:
279:
278:
277:
272:
267:
257:
255:Decision trees
252:
246:
232:classification
222:
221:
220:
217:
216:
213:
212:
207:
202:
197:
192:
187:
182:
177:
172:
167:
162:
157:
152:
147:
142:
137:
132:
127:
125:Classification
121:
118:
117:
114:
113:
110:
109:
104:
99:
94:
89:
84:
82:Batch learning
79:
74:
69:
64:
59:
54:
49:
43:
40:
39:
36:
35:
24:
23:
15:
9:
6:
4:
3:
2:
3905:
3894:
3891:
3889:
3886:
3884:
3881:
3880:
3878:
3861:
3860:
3855:
3850:
3847:
3843:
3840:
3836:
3832:
3828:
3824:
3820:
3816:
3809:
3804:
3803:
3790:
3786:
3782:
3778:
3774:
3770:
3763:
3756:
3748:
3741:
3734:
3726:
3722:
3715:
3708:
3700:
3696:
3692:
3688:
3681:
3672:
3663:
3654:
3645:
3638:
3633:
3631:
3616:
3615:
3610:
3603:
3596:
3590:
3586:
3576:
3573:
3570:
3567:
3566:
3560:
3558:
3554:
3549:
3547:
3531:
3523:
3522:outer product
3507:
3482:
3478:
3474:
3471:
3465:
3456:
3437:
3430:
3404:
3397:
3374:
3370:
3361:
3354:
3350:
3347:
3339:
3332:
3323:
3322:
3317:
3315:
3311:
3310:outer product
3301:
3285:
3277:
3271:
3266:
3262:
3239:
3231:
3225:
3220:
3216:
3192:
3184:
3180:
3171:
3163:
3159:
3153:
3143:
3138:
3133:
3129:
3108:
3086:
3076:
3073:
3065:
3058:
3054:
3046:
3039:
3016:
3006:
3003:
2994:
2977:
2971:
2968:
2942:
2934:
2930:
2926:
2918:
2910:
2907:
2901:
2893:
2889:
2884:
2876:
2875:
2874:
2860:
2857:
2854:
2851:
2848:
2845:
2823:
2820:
2817:
2809:
2806:
2803:
2800:
2797:
2794:
2788:
2777:
2771:
2768:
2761:
2746:
2727:
2721:
2718:
2714:
2710:
2707:
2685:
2679:
2673:
2669:
2665:
2643:
2639:
2631:Furthermore,
2629:
2613:
2602:
2599:
2594:
2590:
2581:
2577:
2568:
2564:
2541:
2536:
2532:
2509:
2505:
2478:
2474:
2468:
2463:
2459:
2455:
2450:
2446:
2441:
2435:
2430:
2426:
2405:
2398:has variance
2383:
2379:
2371:The estimate
2369:
2355:
2330:
2322:
2318:
2314:
2311:
2307:
2303:
2297:
2289:
2285:
2261:
2253:
2245:
2241:
2237:
2234:
2230:
2226:
2220:
2212:
2208:
2201:
2196:
2193:
2190:
2180:
2175:
2171:
2163:
2162:
2161:
2147:
2124:
2118:
2110:
2106:
2100:
2097:
2091:
2083:
2079:
2074:
2070:
2065:
2062:
2059:
2055:
2047:
2046:
2045:
2026:
2023:
2019:
1995:
1992:
1983:
1969:
1944:
1940:
1931:
1927:
1901:
1897:
1888:
1884:
1861:
1857:
1847:
1831:
1827:
1804:
1800:
1776:
1773:
1761:
1755:
1750:
1746:
1722:
1710:
1704:
1699:
1695:
1672:
1668:
1664:
1661:
1658:
1653:
1649:
1626:
1622:
1618:
1615:
1612:
1607:
1603:
1582:
1579:
1576:
1573:
1570:
1567:
1547:
1527:
1491:
1485:
1482:
1473:
1465:
1461:
1457:
1449:
1441:
1437:
1433:
1430:
1426:
1385:
1381:
1354:
1351:
1348:
1344:
1317:
1313:
1289:
1283:
1275:
1267:
1245:
1239:
1236:
1227:
1219:
1215:
1211:
1206:
1202:
1165:
1161:
1138:
1134:
1125:
1121:
1100:
1094:
1091:
1088:
1071:
1048:
1042:
1031:
1020:
1019:hash function
1016:
1015:
1014:
1006:
1004:
1000:
996:
991:
989:
985:
980:
978:
974:
970:
966:
962:
958:
955:is a type of
954:
943:
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3863:. Retrieved
3859:ResearchGate
3857:
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3687:Pagh, Rasmus
3685:Ninh, Pham;
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3618:. Retrieved
3614:ResearchGate
3612:
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3575:Tensorsketch
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988:median trick
981:
953:Count sketch
952:
951:
819:PAC learning
506:
355:
350:Hierarchical
282:
236:
230:
3846:IEEE Access
3727:(3): 50–53.
3595:IEEE Access
3321:convolution
3314:convolution
2277:The values
1272:exhibits a
997:, bilinear
703:Multi-agent
640:Transformer
539:Autoencoder
295:Naive Bayes
33:data mining
3877:Categories
3865:2020-07-11
3749:: 108–109.
3620:2020-07-11
3581:References
1687:such that
1511:will work.
973:AMS Sketch
969:algorithms
961:statistics
688:Q-learning
586:Restricted
384:Mean shift
333:Clustering
310:Perceptron
238:regression
140:Clustering
135:Regression
3835:0304-3975
3789:119661450
3532:⊗
3475:⊗
3351:∗
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3275:‖
3236:‖
3229:‖
3139:∗
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3007:∈
2972:∈
2821:×
2795:−
2789:∈
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1982:th hash.
1774:±
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1458:⋅
1408:}. Since
1212:⋅
1092:⋅
847:ECML PKDD
829:VC theory
776:ROC curve
708:Self-play
628:DeepDream
469:Bayes net
260:Ensembles
41:Paradigms
3689:(2013).
3563:See also
3544:denotes
3389:, where
3121:we take
2497:, where
1124:variance
270:Boosting
119:Problems
3520:of the
1919:to the
999:pooling
852:NeurIPS
669:(ECRAM)
623:AlexNet
265:Bagging
3833:
3787:
3149:median
2186:median
2044:where
1184:, the
645:Vision
501:RANSAC
379:OPTICS
374:DBSCAN
358:-means
165:AutoML
3811:(PDF)
3785:S2CID
3765:(PDF)
3743:(PDF)
3717:(PDF)
2008:sums
867:IJCAI
693:SARSA
652:Mamba
618:LeNet
613:U-Net
439:t-SNE
363:Fuzzy
340:BIRCH
3831:ISSN
3551:The
3422:and
3254:and
2961:for
1819:and
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1641:and
1540:and
967:and
877:JMLR
862:ICLR
857:ICML
743:RLHF
559:LSTM
345:CURE
31:and
3823:doi
3819:312
3777:doi
3695:doi
2556:is
1001:in
603:SOM
593:GAN
569:ESN
564:GRU
509:-NN
444:SDL
434:PGD
429:PCA
424:NMF
419:LDA
414:ICA
409:CCA
285:-NN
3879::
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